What are your current research interests?
My field of study of dynamics equations on time scales and my expertise is oscillation criteria. Calculus is an area of mathematics that helps us understand the changes in values that are related by a function. There are two types of calculus: differential and integral. Differential calculus focuses on breaking things into small (different) pieces and tells how these pieces change from one point in time the next. On the other hand, integral calculus joins (integrates) those small pieces and tells how much of something is made because of the changes. These happen on the real line.
Time scale calculus allows us to differentiate (break apart) and integrate (put together) on any non-empty closed subset of the real numbers ℝ. We call this set a time scale. When we read "subset of the real numbers," think "some part of the number line." So, you do not have to use the number line; you can use any part of it. For example, you could use just the natural numbers – 1, 2, 3, etc. To say a set is closed means the set has all its limit points. Now what is a limit point? Informally, think of a limit point as a point that some sequence of other points (in the set) approach as time goes on.
My current research focuses on applying time scales to model intermittent androgen deprivation therapy for prostate cancer. Prostate cancer is a common cancer among males in the United States and is often treated by intermittent androgen deprivation (IAD) therapy. This therapy requires a patient to alternate between periods of androgen suppression treatment and no treatment. During this therapy, there is a pause between treatment cycles. Traditionally, continuous ordinary differential equations are used to estimate prostate specific antigen levels, which determine the timing of a pause. The goal is to use dynamic equations to estimate prostate specific antigen levels and construct a time scale model to account for both continuous and discrete time simultaneously. This is necessary to account for breaks between treatment cycles.
My second research interest is STEM (science, technology, engineering, and mathematics) education and training. I am extremely interested in implementing and running STEM programs that ultimately increase the number of students, especially those from underrepresented groups, earning bachelor's degrees in STEM fields and doctoral degrees in mathematics. I am currently serving as an associate director of the TTU (Texas Tech University) STEM Center for Outreach, Research, and Education and a co-director of the EDGE (Enhancing Diversity in Graduate Education) Program.
What types of outreach and engagement have you been involved with?
Much of my outreach and engagement have been focused in the areas of STEM education and training and diversity. On the university level, I have led a workshop for the annual Emmy Noether High School Mathematics Day since 2012. This day aims to provide women students with a unique, high-quality experience designed to foster interest in mathematics and careers in mathematics, engineering, and science. I also serve as the faculty advisor, since 2014, of Young Women in Mathematics, now the AWM (Association for Women in Mathematics) Raiders, the TTU Chapter of AWM.
Professionally, I belong to several professional societies including AWM, the National
Association of Mathematicians, and the Society for Industrial and Applied Mathematics (SIAM). My initial service to SIAM was student and junior faculty centered by chairing and serving as a member of the Workshop Celebrating Diversity. This annual event provides minority graduate students and junior faculty with the opportunity to showcase their research and to expand their professional network by meeting people from various professional backgrounds including academia, national laboratories, industry, and government.
My engagement with SIAM continues with the fellow co-founders of the website Mathematically Gifted and Black (MGB). In collaboration with SIAM, we are working to establish a fellowship to recognize the achievements and to support the work of early-career applied mathematicians from underrepresented racial and ethnic minority groups in the mathematical sciences. This began during summer 2020 from MGB's clear stance of supporting Blacks in America in the wake of the acknowledgement of repeated systemic racism. Mathematically Gifted and Black highlights the contributions and lives of Black mathematicians. The mathematicians featured have made significant contributions in research, mentoring, and teaching. The website has been recognized by the American Mathematical Society as a "celebration the diversity of Black mathematicians," and the National Math Festival describes it as a resource that "provides access to the diverse and dynamic community of black mathematicians."
Greater still is my work with the EDGE Program, which is a Presidential Award for STEM Mentoring recipient. EDGE aims to strengthen the ability of women students to successfully complete PhD programs in the mathematical sciences and place more women in visible leadership roles in the mathematics community. Currently, there are 107 EDGE PhDs. After being a participant in 2002, I returned in 2014 to be a course facilitator. I taught four consecutive summers and became co-director in September 2017. In summer 2018, Texas Tech hosted the EDGE Summer Session. It is great to be supported by an institution with a "long-standing commitment to diversity and enhancing participation and of women and other underrepresented groups in STEM fields" as said by Mark Sheridan, dean of the Texas Tech Graduate School in "Summer Program Gives Women in Graduate -level Mathematics an EDGE" in Texas Tech Today.
Why did you choose this field?
Math chose me. I was an average student at math in elementary and middle school. I became good at math in 8th grade as result of having an A-M-A-Z-I-N-G Algebra I teacher. Her name is Mrs. Gwendolyn Scott. She knew I had not taken Pre-Algebra, but she knew I had the ability to learn the material and excel. Mrs. Scott gave me extra work, moved my seat, and required that my graded assignments be signed by my parents. That bit of extra motivation was what I needed, and I became an aspiring mathematician.
After having such a positive experience in Algebra, I wanted to change students' lives like Mrs. Scott had changed mine. So, my plan was to be a math teacher. Once I got to college at Xavier University of Louisiana, my advisor, Dr. Vlajko Kocic, encouraged me to explore my options outside of teaching. He talked to me about graduate school. I had some idea of what graduate school was because my father, who is a retired high school teacher, has a master's degree in Industrial Arts Education. I recall him going to class and doing homework. So graduate school was not a new idea. The idea of earning a doctorate was. Dr. Kocic told me that I was going to graduate school and I worked to achieve that. At Xavier, there were upper class female math majors who were going to graduate school and who were doing well. So, his suggestion of graduate school seemed reasonable. Honestly, it was the norm, the expectation, the rule, the standard.
How do you define good teaching?
Good teaching begins with caring about students as learners. As no two people learn the same, it is paramount that students are able to find an entry point into the course content. This requires me to meet my students where they are, not where I expect them to be. Good teaching continues with clearly explaining course content based on the skills and abilities of the students. Mathematics is a subject that builds on itself – layer upon layer. It will be nearly impossible for students to further their learning if I do not first meet them where they are. At times this requires covering material not directly related to the course. Once the class' foundation is reinforced, good teaching challenges students. The goal is to develop critical thinkers, students who take ownership of the material, ask questions, and have the tools to develop new solutions.
What is your proudest professional accomplishment?
It is hard to choose just one. However, I would say my selection as the winner of the 2021 M. Gweneth Humphreys Award for Mentorship of Undergraduate Women in Mathematics by the Association for Women in Mathematics. This award recognizes outstanding accomplishments in encouraging and mentoring undergraduate women. I chose mathematics and academia to impact young women just as I was by my eighth grade Algebra teacher. It is so rewarding to be living my dream and humbling to know that others recognize and appreciate my contributions.
How do you integrate research and outreach into teaching?
Integrating research has been manageable as I was introduced to my research as undergraduate. Since my area is related to calculus, I can show students, especially undergraduates, how foundational courses are needed to do high-level research. Integration outreach happens anecdotally. I share the types of activities that I'm passionate about and encourage students to pursue their own "passion work".
More About Raegan Higgins
Raegan Higgins, Ph.D., is an Associate Professor of Mathematics in the Department of Mathematics & Statistics at Texas Tech University. Her current research focuses on oscillation criteria for dynamic equations on time scales. While she is also interested in applications of fractional calculus, Dr. Higgins has a keen interest in increasing the number women, especially those underrepresented, in STEM. She is a proud alumnus of Xavier University of Louisiana. In 2008, Dr. Higgins was one of the first two African-American women to earn a doctoral degree in Mathematics from the University of Nebraska- Lincoln.
A native of Baton Rouge, LA, Dr. Higgins was named one of the 2016 Inspiring Women in STEM by INSIGHT into Diversity. This award recognizes women who work to inspire and to encourage the next generation to pursue STEM education and careers. Because of her own experience pursuing a STEM degree, Raegan understands the importance of creating supportive environments where underrepresented students can thrive. This passion has led to her programs and projects such as Enhancing Diversity in Graduate Education and website Mathematically Gifted and Black.
Understanding the importance of service, Raegan is active in her community. She is the immediate past- president of the Lubbock Alumnae Chapter of Delta Sigma Theta Sorority, Incorporated. Under her leadership, the Delta GEMS and Delta Academy programs have been reintroduced. While Academy focuses on young adolescent females and GEMS on young ladies over 14, both aim to prepare them for full participation as leaders in the 21st century. As an advocate for students, she is a mentor in Mentor Tech and the campus advisor of the Eta Lambda Chapter of Delta Sigma Theta at TTU. Additionally, Raegan is the director of math tutoring at her church. She was inspired to assist after hearing some of the math challenges of her church's middle schoolers.
Raegan and her handsome husband, Dr. Kamau Oginga Siwatu, are the proud parents of two lovely children. Their daughter, Jalia, is an inquisitive ten-year old and son, Tendaji, is a fun-loving second grader.