Guiding Principles for Equity-Oriented Professional Development for Mathematics Graduate Teaching Assistants

Instruction that is active and attends to diversity, equity, and inclusion (DEI) has become increasingly important in mathematics education. As teaching assistants, graduate students impact the mathematical experiences of thousands of undergraduate mathematics students SM15. Therefore, their professional development and growth as educators is critical, especially when considering that many graduate teaching assistants pursue careers in teaching mathematics. In this paper, we share guiding principles for developing a mathematics graduate teaching assistant (MGTA) professional development program that focuses on active learning and diversity, equity, and inclusion. Importantly, we ground this work in DEI, rather than having DEI as a one-time or add-on component. Further, we demonstrate the implementation of a professional development program that we designed using these principles. We briefly discuss how we adapted this program at three institutions and how we, as instructors of this professional development, have supported MGTAs’ growth as teachers in enacting active, diverse, equitable, and inclusive classroom practices. We share our thoughts on effective professional development for mathematics graduate teaching assistants in advancing their understanding of active learning and equitable teaching by highlighting elements of the program that are shared across our institutions.

1. Introduction

In recent years, there have been continual calls for active learning with attention to DEI especially for the teaching preparation of MGTAs, as they typically teach or support lower-level large enrollment courses GBR16MAA18SM15. These calls are motivated by the persistent inequities present in the structures and systems within and surrounding mathematics classrooms. For instance, Berry (2021) observed that historically excluded learners are “routinely given the least access to advanced mathematics content” and “the least access to well-prepared mathematics teachers” (p. 3). These inequities hinder students, especially those underrepresented in science, technology, engineering, and mathematics (STEM), from experiencing a deep sense of belonging and empowerment within STEM education.

Active learning has shown promise to positively impact student performance, among other important aspects of equity. For example, in undergraduate STEM courses, Freeman et al. FEM+14 found “students in classes with traditional lecturing were 1.5 times more likely to fail than were students in classes with active learning,” and Theobold et al. THT+20 report that the average difference on exam scores between minoritized and nonminoritized students was SD=-0.42 for active learning classes and SD=-0.62 for traditional lecture. Similarly, the gap in passing rates among these students for active learning classes was 3.9%, which was a drop from 7.1% for traditional lecture classes THT+20.

Recent data from Braley et al. BBGS23 indicate that mathematical sciences departments are beginning to support the professional development (PD) of MGTAs through orientation and first-year teaching seminars, and, in some cases, yearlong courses about teaching.⁠¹ We see this growth of PD in departments as a positive shift. At the same time, MGTAs are unlikely to implement teaching practices that support active learning and DEI-related practices in the first year of their graduate programs and need time to adjust to the routines of teaching before adopting teaching practices they have not yet experienced BGR19Mil18. Moreover, MGTAs have traditionally received little training in pedagogy or on DEI issues DHS15SDE17.

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The CoMInDS website provides many examples of MGTA PD programs and materials: https://connect.maa.org/communities/community-home?CommunityKey=cc0d52e1-9a32-429c-8f97-d5f71a6d9b54.

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We argue that impactful and sustained change in active learning and DEI-related practices involves an ongoing reflective process grounded in practical scenarios and narratives that connect to graduate student experiences. We provide an example of MGTA PD that extends beyond the first year and focuses on active learning, equity, and inclusive teaching practices. Given the impact of MGTA training, the need for ongoing PD, and the necessity that these focus on active learning and DEI, our work is an important step forward in MGTA PD and a valuable contribution to mathematics education. Moreover, research shows that teaching experiences help to develop graduate students’ research skills in STEM and prepare them for a research career SE18. The design of our PD program is informed by four guiding principles, which we describe in the next section.

2. Guiding Principles for and Assumptions about Engaging MGTAs in Equity-Focused Professional Development for Teaching

In developing a PD program to support MGTAs, we identified and addressed common assumptions made about and by MGTAs. These principles guide us in our work as we structure our respective PD programs and create PD activities for MGTAs.

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Guiding Principle 1 (GP1): MGTAs need a safe community to engage in critical conversations.

It is important to create a consistently safe space for critical conversations where participants feel valued, recognized, and understood. Discussions around themes of equity and inclusion can feel uncomfortable at times, so creating a safe space where MGTAs feel brave enough to grapple with tension or discomfort is critical.

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Guiding Principle 2 (GP2): MGTAs have a diversity of backgrounds, experiences, expertise, and goals.

We recognize that MGTAs do not come to us as “blank slates.” They are individuals with past experiences, knowledge, expertise, and goals for their teaching and students. MGTAs have unique and complex identities that should be celebrated and leveraged, which impact how they develop and enact their own pedagogy.

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Guiding Principle 3 (GP3): Because MGTAs are diverse, there are multiple roads and timelines to equitable teaching and learning.

We recognize that MGTAs will enact equitable and inclusive teaching practices in their own ways—finding their voice as teachers. Thus, it is important to meet MGTAs where they are by supporting the development of teaching practices that are in alignment with their teaching goals. As such, a myriad of activities should be employed that cover a breadth of ideas and goals related to active learning, equity, and inclusivity. Activities will resonate differently with each MGTA, and in conjunction with their background, will uniquely manifest active, equitable, and inclusive practices in their classroom. As part of this work, it is important to acknowledge that change does not happen overnight; growth in teaching takes time.

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Guiding Principle 4 (GP4): MGTAs grow in their teaching by engaging with practical scenarios, student narratives, and experiential activities.

To support growth in teaching, we draw from the literature on active learning, which advocates for instruction that promotes student engagement. Similarly, learning about equity and inclusivity is not effectively accomplished by only reading theory or watching presentations. While this information (and mode of dissemination) can be valuable, ongoing engagement with and discussion about teaching practices must inspire critical reflection of the lived realities of students, especially those who are historically marginalized or vulnerable. Engaging with practical scenarios, student narratives, and experiential activities provides opportunities for MGTAs to practice and reflect upon their teaching and develop a deeper understanding of and empathy for the students in their classroom.

In the same way that we employ these principles in the PD program we offer the MGTAs (as our students), we hope that these ideas translate to the MGTAs’ classrooms.

3. ELITE PD—An Example of the Guiding Principles in Action

In this section, we describe a PD program that we developed using these principles. At our respective universities, we employ the Engaged Learning, Inclusive Teaching, and Equity PD (ELITE PD) program, which is a multi-course PD program for MGTAs (for more information and resources, including institutional adaptations, visit our website at https://elitepd.sdsu.edu/). Currently, ELITE PD courses are taught by mathematics department members (e.g., faculty, postdoctoral scholars) with experience participating in or facilitating PD workshops, activities, or community dialogues focused on active learning and equitable practices (e.g., CoMInDS; university-specific equity training).

The MGTAs who participate in this program include master’s and doctoral students, with duties ranging from those who are instructors of record to those who only grade and hold office hours, and, though rare, to those who teach in an online setting. The most common role for our MGTAs is one of leading recitation-style sections that meet one to two times per week with up to about 40 students. The components of ELITE PD are Orientation (prior to the first term of teaching), Graduate Teaching Seminar, Introduction to Equity and Active Learning course, Advanced Equity and Active Learning course, and Peer Mentoring. The broad learning goals of the program are:

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MGTAs will gain an understanding of their department, their role as an assistant within the department, and campus resources. (Departmental knowledge)

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MGTAs will work to develop a sense of community and belonging among their graduate student cohort. (Community)

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MGTAs will gain a greater awareness of the diversity of experiences and access of undergraduate mathematics students. (Diversity, Equity, Inclusion)

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MGTAs will gain experience with evidence-based teaching practices with a focus on active learning, equity, and inclusion. (Practice)

As previously stated, a notable feature of this program is that active learning is not treated separately from equitable and inclusive practices. Rather, it is grounded in equity and inclusion. It is not sufficient, for example, to just put students into groups and have them work on problems. Instead, in order to mitigate inequities in the classroom that can arise in active learning classrooms, Reinholz et al. RJA+22 advocate for careful implementation of such practices with a focus on attending to equity and inclusion.

In the ELITE PD program, MGTAs begin with Orientation, which takes place 2–4 days prior to the start of the term (semester or quarter). During Orientation, MGTAs learn about the department and their roles, engage in community building with their peers, develop introductory knowledge of teaching practices focused on active group learning and dynamics, basic classroom logistics (e.g., board work), and expand their awareness of the diversity of experiences and access needs of undergraduate mathematics students. Once the term starts, MGTAs take the Graduate Teaching Seminar where they are actively engaged in learning about the department, the university’s teaching support resources, classroom management, and how to implement small-scale instructional practices with attention to equity, inclusivity, and active learning. The next component in the ELITE PD program is the Introduction to Equity and Active Learning course during which MGTAs continue to build upon their understanding of and facility with active learning and equitable teaching practices. The last course, Advanced Active Learning and Equity, has MGTAs engaging with specific research-based pedagogical approaches as well as equity research associated with teaching. Additionally, throughout the ELITE PD program, MGTAs are observed in their classroom and are provided feedback about their teaching. Once coursework is completed, MGTAs can then serve as peer mentors to new MGTAs entering the program.

4. Samples of Activities in ELITE PD

Table 1 provides samples of activities involved in the ELITE PD courses.

In order for these courses to be productive for MGTAs, ELITE PD course instructors take actions to co-construct a safe and confidential space by discussing the desired classroom and conversation norms (GP1). Throughout each ELITE PD course, we enact a variety of activities intended to support MGTAs in considering DEI issues from multiple perspectives and theories (e.g., critical race theory, access, meritocracy, microaggressions) (GP3). We also anticipate that different activities will resonate with some MGTAs more than others due to their individual backgrounds and experiences in education (GP2, GP3), and therefore we provide MGTAs with the freedom to explore equitable teaching practices in alignment with their own goals for teaching (e.g., Lesson Plan Activity, Active Learning Presentations) (GP3). Notably, MGTAs are often engaged in an active learning experience themselves, as almost every activity in the ELITE PD courses has an experiential or practical feature (GP4).

We structured these courses so that MGTAs begin by considering different student situations (Orientation and Graduate Teaching Seminar), reflect on their identities and how identity impacts the mathematics classroom (Introduction to Equity and Active Learning), and understand more deeply how systems of oppression such as racism, sexism, and ableism impact education (Advanced Equity and Active Learning). As a note, the activities mentioned can be shifted around based on local context and the MGTAs. In Table 1 we highlight example activities with associated GPs. Throughout each activity, we make a point to center the conversation around the classroom and experiences of students.

The role of the PD instructor

Like with any other course, ELITE PD instructors hold office hours for MGTAs to support them in their growth as teachers. MGTAs attend these hours, as needed, to get additional support for their teaching-related concerns and questions. In conjunction with the PD courses, these hours provide spaces for MGTAs to unpack their own identities (as much as they are comfortable) and reflect on their positioning in the classroom (GP1). For example, MGTAs discuss how to navigate their 2SLGBTQIA+⁠² identities in their teaching, grappling with how much to share with their students and how much they keep private. These practices by PD instructors provide MGTAs the opportunity to reflect on their teaching practices in a safe space (GP1). In addition to conversations, PD instructors also observe MGTAs’ teaching and regularly follow up with MGTAs on their teaching ideas—encouraging MGTAs to try out their ideas and ask them how those ideas are going (GP3).

²

Two Spirit, lesbian, gay, bisexual/bigender/biromantic, transgender, queer, intersex, agender asexual/aromantic, and other gender and sexual minorities.

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MGTAs’ takeaways from ELITE PD

As a result of their participation in ELITE PD, MGTAs have expanded their thinking related to teaching, DEI, and classroom issues SYS+24. In Table 2 we provide some examples of MGTAs’ feedback on the ELITE PD courses.

From MGTAs’ feedback, we see evidence of the impacts of each guiding principle. MGTAs felt comfortable being vulnerable when sharing ideas (GP1), developed unique equity-oriented goals and strategies for their own concerns as well as valued the varying perspectives of their peers and the different ways that their peers may implement activities (GP2, GP3), and consistently appreciated and recalled the practical and tangible activities that transformed their teaching (GP4). Preliminary analysis of classroom observation data validates MGTAs’ own reflections of transformational changes in their teaching. Key to these transformations were ELITE PD course discussions. We regularly observed MGTAs engaging in critical conversations and thinking deeply about complex ideas around equity and inclusion, which fostered a community of practice as MGTAs discussed ideas with each other. Moreover, MGTAs recognized that not all students in their classroom were the same nor had the same past experiences, and acknowledged students’ unique needs. Overall, we have noticed MGTAs’ growth in knowledge of how equity and inclusivity are approached in teaching. MGTAs began with broad ideas about students coming into the classroom, and developed specific thoughts about underlying assumptions regarding coursework and how those assumptions and corresponding coursework impact students. MGTAs’ growth is further evidenced by our preliminary analysis of student survey data, which shows increases in students’ sense of belonging and active engagement in the classroom. In addition, we saw MGTAs’ student evaluation scores increase over the course of a year.

5. Final Thoughts

In closing, we want to emphasize that MGTAs contribute to the learning experiences of thousands of students at each institution each year. Their potential impact in the classroom is nontrivial, and their growth as teachers should be valued. Preliminary findings show that over the course of an academic year, ELITE PD MGTAs are 1) implementing and sustaining learned teaching practices (e.g., quality group work norms), 2) improving in their abilities to promote students’ sense of belonging and active engagement in the classroom, and 3) receiving better student evaluations over the course of a year. Thus, for MGTAs to adopt student-centered, inclusive, and equitable teaching practices, it is imperative that they receive ongoing PD that extends beyond a single term. We offer these four guiding principles that center equity, inclusivity, and active engagement, so that other change agents, MGTA coordinators, and PD providers can adopt them into their existing programs.

Table 1.

Examples of activities within ELITE PD courses.

ELITE PD Course	Examples of associated activities and emphasized guiding principle(s)
Orientation	$\vartriangleright$ Mobile Activity (adapted from SD14)
	This activity supports MGTAs in developing awareness of differences in students’ experiences and empathy for students. MGTAs are put into groups where each group has a hanger and a bag of craft items. Bag contents vary in the amount of resources and range from a single crayon, piece of string, and a paperclip to stickers, colorful string, scissors, glue, and an array of crayons and markers. Each group is tasked with creating a mobile (structure that hangs above a baby crib) using the contents in their respective bags. Each group is expected to achieve the same result but with different “resources,” which leads to groups experiencing frustration. This primes MGTAs for a conversation about the students in their classroom during which resources, access, and assumptions are topics of focus. (GP2, GP4)
	$\vartriangleright$ Campus Counseling and/or Disability Services Discussion
	Representatives from the respective offices/departments converse with the MGTAs. This supports MGTAs in developing awareness of support services available on campus for both their students as well as themselves. (GP1, GP4)
Graduate	$\vartriangleright$ Classroom Norms Building Activity
Teaching Seminar	MGTAs co-construct norms for the Graduate Teaching Seminar with the instructor, and then discuss how they will construct norms for the classes that they teach. (GP1)
	$\vartriangleright$ Advantages Checklist⁠3 3 Advantage Checklist towards Educational Equity ©2024 by Jamiella Brooks, licensed under CC BY-NC 4.0 ✖
	MGTAs fill out a checklist tied to advantages and privileges. MGTAs identify personal advantages and privileges, then reflect and discuss with a partner how issues of privilege impact student success in education. The activity concludes with a whole-group discussion where MGTAs are asked to share how lack of access to advantage(s) might show up in a classroom and how course design could negate the lack of advantage(s), enabling a more equitable and inclusive environment. (GP2, GP4)
	$\vartriangleright$ The Silhouette Activity
	This activity is focused on unpacking dimensions of identity of self (visible and invisible). MGTAs are given a handout that has the outline of a head or hand. They then write on the inside or outside of the silhouette aspects of their identity that are visible and invisible. This then expands into a discussion of student identity (visible and invisible) through classroom scenarios. (GP2, GP4)
Introduction	$\vartriangleright$ Majority and Marginalized Identities Activity
to Equity and Active Learning	MGTAs fill out a checklist, selecting ways they see themselves as in a majority or marginalized identity group. In groups, MGTAs then reflect and discuss how these identities are connected to power and privilege as instructors and students. They then connect these ideas to their students and reflect on how they may want to adapt their teaching to support different student groups. (GP2, GP4)
	$\vartriangleright$ Microaggressions Vignettes
	MGTAs read classroom scenarios involving microaggressions and discuss action plans and responses to issues in the classroom. Scenarios have been developed from mathematics classrooms—we highlight context-specific issues that have arisen, and incorporate Francis Su’s “Mathematical Microaggressions.” (GP4)
	$\vartriangleright$ Observation Activity
	MGTAs observe their peer’s classroom and reflect on the extent to which active learning, inclusive, and equitable teaching practices are present in the lesson they observe. (GP3, GP4)
	$\vartriangleright$ Lesson Plan Activity
	MGTAs develop an active learning-oriented activity for their class and present on their activity. (GP3, GP4)
Advanced Equity	$\vartriangleright$ Band-Aid for Bullet Holes
and Active Learning	MGTAs read and discuss narratives from disabled students about access and accommodation experiences with their university. MGTAs then connect these experiences to their own teaching, discussing perceptions and issues related to access. (GP4)
	$\vartriangleright$ Examining Problematic Questions and Tasks
	MGTAs examine “objective assessments” and discuss how they might be biased towards one population (and thus are not objective assessments), such as the SAT®“regatta” analogy question:
	RUNNERS: MARATHONS
	A) envoy: embassy
	B) martyr: massacre
	C) oarsman: regatta
	D) horse: stable
	MGTAs examine mathematical tasks with complex vocabulary and jargon—discussing assumptions and interpretations they made in order to answer the questions. MGTAs then discuss how students with various backgrounds will engage with the tasks. (GP2, GP3, GP4)
	$\vartriangleright$ Active Learning Presentations
	MGTAs individually read or watch a video on specific active learning practices such as Think-Pair-Share, Jigsaw, Concept Attainment, and Chat Stations, then present that teaching strategy and provide an example of how they might implement it in their classroom. (GP3, GP4)

Table 2.

A selection of MGTA ELITE PD participant quotes.

ELITE PD Course	MGTA ELITE PD Participant Quotes
Orientation	“…it shouldn’t be assumed that everyone begins equally, and everyone brings their own unique situation and access to resources to everything they do” (Mobile Activity Exit Ticket)
	“Honestly, I’m terrified that I succumb to cognitive biases and socially conditioned prejudice. I work on it a lot. I try to learn about other peoples’ cultures, truly hear their concerns, and refrain from dismissing someone’s voice or agency. However, it is unrealistic to truly eliminate all my blind spots. I think about this often. I recoil from the idea that my actions may in some way inhibit a student from becoming equipped. Further, whenever I go to a conference about or get trained in or discuss this topic, it is always in the abstract. Very rarely do I have specific examples. I feel that act-outs or dissecting specific real-life examples would go a long way for me. In general, I hope that personal relationships with students will help to mitigate this. If someone feels comfortable confronting me, then I don’t have to know everything already.” (End-of-Orientation Survey)
Graduate Teaching Seminar	“This course changed the way I view teaching for the better. It made me more aware of the unique needs and experiences of my students. The most important thing I learned is that my job is more than just teaching. I learned that there are ways to help students have a positive view of math and help them realize they have worth regardless of academics.” (End-of-term Survey)
Introduction to Equity and Active Learning	“…the observation activity, which was particularly effective for me because it connected the physical (i.e., actually being in the classroom), to the theoretical—looking for concrete examples of someone applying (or not) a certain theory.” (End-of-term Survey)
	“I really liked designing activities and hearing what other people come up with. Anywhere I can start doing what we learn about and see others do what we learn is awesome, so more of the “doing” stuff.” (End-of-term Survey)
Advanced Equity and Active Learning	“I thought the activity [with] different classwork/exam examples and pointed out assumptions was very impactful on the way I word my questions to students.” (End-of-term Survey)