Dr. Juan B. Gutiérrez, Chair of Mathematics

Mathematics is everywhere. Mathematics is for everyone. Mathematics is the alphabet with which the vocabulary of all sciences is built. It is no surprise that the Department of Mathematics is among the largest at UTSA by number of students and credit hours served, and therefore it has a large contribution to student success. We serve approximately 12,000 seats per year.

One of the best predictors of success across domains is numeracy coupled with confidence. Our society pays a tragic human cost when students drop out from UTSA and never finish their degrees, or end up in different destination majors that do not match their passion and greatest contribution potential. In many cases, mathematics is the greatest obstacle.

The Department currently has experts in multiple areas of research. It offers three Bachelor of Science degrees: the B.Sc. degree in General Mathematics Studies, the B.Sc. degree in Mathematics, and the B.Sc. degree in Mathematics of Data and Computing offered as a joint degree with the Department of Computer Science. The Department also offers three Master of Science degrees: M.S. in Applied Mathematics–Industrial Mathematics, M.S. in Mathematics, and M.S. in Mathematics Education. The Department is engaged in the creation of a Ph.D. program.

In terms of research, our department is growing its connections to many other academic units. We recognize the importance of (i) pure mathematics as the foundation for mathematical research, (ii) applied mathematics as a highway for interfacing with other academic units, and (iii) mathematics education as the driver to understand instruction and learning. The Department will maintain a balanced research portfolio in these areas.

UTSA is unique in its diversity and how it reflects the society it serves. We can contribute to have the face of success match the face of society. Access to and achievement in STEM fields (Science, Technology, Engineering and Mathematics) is not evenly distributed among all members of the US society. The National Science Foundation keeps reliable annual statistics in this subject (available here). The Department of Mathematics is working to provide a template to the nation for closing achievement gaps.

Improvements in mathematics education at the undergraduate level are having an impact in all STEM education and research at UTSA. We recognize this opportunity, thus we are engaged in a continuous improvement process in teaching. We are building a department that facilitates even access to the opportunities that come with higher education, and we are doing it through education and research in mathematics.

Currently, UTSA is undergoing a profound and positive transformation. The most evident change is the designation as a research-intensive (Carnegie classification R1) institution in 2022. The growth the university is experiencing in all aspects (diversity, achievement, number of students and faculty, financials, endowment, research, academic quality, etc.) supports the idea that The University of Texas at San Antonio is the university of the future.

In the plot below, Donors are on the left: Majors where students begin. Acceptors are on the right: Where students end up. Poor performance in entry-level mathematics courses has a large correlation with abandoning STEM. p-value << 1E-5

**Strategy**: We increased support in entry-level math to counter this trend. With support from the College of Sciences, we tripled our Teaching Assistant workforce in two years.

In the plot below, each circle represents faculty member. The horizontal axis is the course code, from 500 to 4999. The radius of each circle is proportional to the number of students served by each faculty member. There was a huge disparity between faculty teaching the same course in terms of DFW.

**Strategy**: We enacted course coordination to counter this trend.

In the plot below, each circle represents faculty member. The horizontal axis is the total number of students served. The radius of each circle is proportional to the number of students served by each faculty member. A cluster on the right reveals faculty with large sections who were generating half of the revenue of the department, and with an average salary of $28,500

**Strategy**: With support from the College of Sciences, we increased salaries of student-intensive faculty to reach national averages (+70% increase for a dozen faculty in 2021).

In the plot below, each circle represents faculty member. The horizontal axis is the total number of students served per each faculty member. The radius of each circle is proportional to the number of students served. There was a huge disparity between faculty teaching the same course in terms of DFW.

**Strategy**: We enacted course coordination to counter this trend.

The Department of Mathematics pioneered in 2020 the simultaneous integration of course coordination and vertical alignment of the curriculum at UTSA. Among the initiatives we implemented are:

- Every lesson in the math curriculum was mapped to prerequisites and student learning outcomes (SLOs). This mapping has been captured in our wiki.
- A course coordinator was selected by their peers for every multi-section course. Course coordinators and course instructors meet once per week to discuss topics, homework assignments, and tests for the classes.
- All test and homework assignments for multi-section courses require a comparable level of effort, and have the same level of difficulty. All multi-section courses advance in lockstep on a weekly basis.
- A common syllabus framework has been developed for the entire Department of Mathematics. All multi-section courses use the same syllabus.

The success of the Department of Mathematics has been possible thanks to the support of the College of Sciences. The Department of Mathematics has produced evidence showing that practices outlined in this article are working. This has elicited a positive response in the institution. In July, 2022, the College of Sciences at UTSA asked all departments in the college to emulate the practices that implemented in the Department of Mathematics. Positive change is propagating.