Mathematics Mentor

Dr. Martha Gregg strives to teach the creative side of mathematics — that the subject demands both “imagination and precise computation.”

The following story by Rachel James Clevenger appears in the August 2014 issue of Private University Products and News and is shared here with permission:

Because her father is a mathematician, Dr. Martha Gregg grew up knowing that math was about more than just numbers and formulas. He would share original questions and puzzles of logic with his daughter, and she delighted in the work.

From an early age, Gregg knew that creative thinking was a part of math too. At Augustana College, she enjoys teaching students about the more creative side of mathematics — that the subject demands both “imagination and precise computation.”

Gregg’s first teaching job was in Tuba City, Arizona, in a high school located on the Dine´ (Navajo) reservation and adjacent to the Hopi reservation. Nearly 97 percent of the student body of 1300 was Native American. Gregg has a personal connection to Native American culture as well, in that her husband is Hopi/Inupiat, and she’s the mother of two Native American children.

However, she is quick to stress that she is “not an expert on Native culture, nor on the teaching of Native students”; in fact, she points out, “The very term ‘Native culture’ is misleading, as each tribal culture is unique, and there are hundreds of tribes.” Though she has been teaching college for several years now, Gregg is grateful for the chance to draw from those experiences in order to serve Augustana students and even some local Sioux Falls students.

Drawing from Native American Culture for Mathematics Education

In 2011, Gregg taught a service learning course for pre-service teachers with the goal of having students “create classroom activities in mathematics which ref lect some aspect of Native culture.” Drawing wisdom from two panels of experienced (mostly Lakota) educators and from cultural consultants as well, students developed activities that ensured the “cultural aspects of their work were accurately, appropriately, and respectfully presented.”

A couple of years later, Gregg had an opportunity to teach a bridge course for five Native American students from Sioux Falls from public high schools; funded by a grant given to Augustana and the SDSU, the pilot program offered two courses for these students, the chance to spend time on the Augustana campus, and mentoring for their college applications. Both courses incorporated Native culture, while also preparing the students for success in college. One of her colleagues, Dr. Eric Wells, sees Gregg’s teaching background as making her “adept at interactions with students of many backgrounds and abilities and their teachers,” as she has applied the experiences working with Native American communities to her work at Augustana.

Taylor Allis is a mathematics and secondary education major at Augustana who begins student teaching in the fall before entering the workforce. Allis shares that she was undecided about her major until Gregg offered to be her advisor. She notes that Gregg is constantly working with her students outside of class time.

“It isn’t out of the ordinary for students to be getting help on a problem during all hours of the day. She will work with you until it clicks, even though she has plenty of other things on her to-do list.”
Taylor Allis
mathematics and secondary education major

Allis believes Gregg’s willingness to always put her students first is part of what makes Gregg an exceptional educator. She adds, “I’ve spent countless hours in her office crying, laughing, telling stories, working through frustrations, and most of all learning.”

Daniel Elmer, who plans to work as an equity or bond analyst upon graduation, has worked with Gregg since his first semester, taking three classes with her and working with Gregg in math club. Though he admires Gregg for any number of qualities—from her patience, her passion for math, and her work ethic—he believes what most separates her from other educators is “her ability to make students want to come to class, as even those people who hate math” still understand that she is a brilliant teacher with her knack of simplifying complicated material into an understandable format. He applauds her ingenuity in the props she chooses for class, using something such as guitar strings to explain math topics that might leave some students confused.

Peder Thompson, a doctoral student in commutative algebra at University of Nebraska-Lincoln, notes that when he first taught Differential Equations at UNL, he drew on what he learned from Gregg in several ways. He shares, “I think much of my excitement for teaching the course came from such an enjoyable experience in Dr. Gregg’s class just a few years prior. One topic in Differential Equations that particularly stuck with me was Laplace Transforms; my students asked why I was so excited about teaching them, and I told them that I had enjoyed learning about them so much from my own professor and wanted to pass on that same enthusiasm for mathematics."

Dr. Wells commends Gregg for her skill in incorporating active learning into traditionally didactic, proof-based courses. In one of her classes that Wells observed, Gregg worked an assignment with predefined groups, with each group presenting proofs simultaneously. He notes, “The trick was that all the proofs were related. When they were finished, the group discussion examined the similarities and differences in the proofs, and thus more material was covered than would be possible in the same amount of time by a single instructor working didactically.”

Learning to Teach

When she started her master’s degree, Gregg notes that a weekend-long preparation was customary to prepare graduate teaching assistants. In her weekend prep sessions, she and other graduate students were given plenty of advice on expectations for graduate students, common stresses for graduate students, and even dealing with the university. Gregg found herself thinking, “When are they going to talk about teaching?” Finally, in the last few minutes of the weekend, they mentioned teaching briefly; Gregg could only think, “Oh my gosh, my poor fellow graduate students.”

Even if those students had focused their entire weekend on the act of teaching, though, Gregg recognizes the impossibility of “teaching how to teach” in such a short time and argues for the necessity of an “ongoing supportive mechanism” for mentoring young teachers and graduate students. She also pointed out the irony of the most inexperienced teachers, brand new TAs, often being placed with most inexperienced college students.

A friend of hers told her early in Gregg’s teaching career, “Everybody who teaches has a first year teaching—and it won’t be their best year.” Gregg shares, “I really learned to teach the first three years in the classroom.” She felt privileged to learn from coworkers who had decades of classroom experience to draw on, and she adds she still says things in class that she heard from her first department chair.

Because she taught high school for nine years, Gregg is especially attuned to the difficulties that first-year students might face with the material. For instance, she recognizes that the “speed at which the material comes at them” is quite different, with high school students learning a little bit of new content each day, while college students are expected to have mastered skills learned in Monday’s class and to come prepared to move on by Wednesday’s class. She notes, as well, that it’s a “much more intense, concentrated lesson” in a college lecture, and some students may underestimate how much time they will need to spend practicing the new skill on their own time.

Mentoring and Math Teachers Circles

Gregg has been involved with Project NExT for several years, as a Fellow in 2009 during her second year at Augustana. Project NExT is a national project that connects recent PhD recipients in mathematics and statistics whose goal is to help prepare faculty members in academic careers and mentoring younger faculty. Gregg still goes to the listserv to consult with her fellow NExTers, accessing their advice “again and again and again” from suggestions for textbooks to designs for a new science building to advice on the overhaul of a course. She believes this mentoring is a “great way to start your career and useful to the entire profession.

She has been pleased to see the changes over the years as programs better recognize that colleges and universities are not just charged with helping their graduate students complete their own academic goals—but to turn their teaching assistants into effective educators.

Teaching to Teach

Though she acknowledges that some people may be natural teachers who easily learn from their own mistakes, she recognizes that learning to teach can be challenging for any number of reasons. She also adds, “Teaching somebody how to teach is a very difficult thing to do,” in that differing styles and techniques can be equally effective, yet new teachers would need to find their own styles and strengths through actual classroom experience.

Interestingly, Gregg is a perfect example of continuing to recognize and draw from the experiences of her own mentors, even as she mentors her own students. For the last few months, she’s been working with colleague Eric Wells from the physics department, who has been serving a dual leadership role over both departments, and she will soon step in as chair for the math department. Wells has been handling all of the paperwork, so she can focus on earning tenure, while still bringing in Gregg for all important choices; because of her colleague’s generosity and assistance, she’s been “getting a feel for the sorts of decisions to make” and learning how to focus on the daily details as well as the “big picture” of the department’s plan for the next decades.

One of the ongoing changes they have been focused on within the department is giving their students more research opportunities. Gregg wants to see their students continue to engage with undergraduate research, which requires upper-level analytical tools because “it’s more open-ended, and there’s no answer in the back of the book.” They learn that working on one problem can take months, and she stresses to students who are entertaining the idea of graduate school that the payoff for finding an answer—after potentially expending a great deal of time and energy on one problem—has to be enough for them. Otherwise, she adds, “It’s like applying for a job without knowing the job description.”

Mentoring that Lasts

In recalling his own undergraduate research, Peder Thompson applauds the skillful way Gregg handled his senior thesis project on abstract algebra, as she gave him “exactly the amount of direction” he needed to be successful—intuitively knowing when to step in and when to leave him to work things out on his own. He adds, “This balance of guided learning and independence she provided has served me well in all my work and even into my current research.”

Finally, Gregg’s passion for numbers has also brought her to create a Math Teachers Circle—which works similarly to a book club, but for math lovers. She read about the concept and immediately thought, “Oh, I want one.” Gregg and a group of local educators meet monthly and hash out open-ended problems for a couple of hours over dinner.” Wells shares that Gregg’s work with the local Math Teachers Circle has made her well respected within the local community. He concludes, “She’s a good citizen both within and beyond campus.”