Preparing Graduate Students to Teach Statistics: A Review of Research and Ten Practical Recommendations

Abstract

Many statistics departments in institutions throughout the world hire graduate students to teach and assist with the teaching of undergraduate and graduate-level statistics courses. As many of these graduate student instructors and graduate teaching assistants (GTAs) have little or no previous experience teaching statistics, statistics departments are faced with the challenge of preparing their graduate students for teaching roles. Articles have been written sharing various departments’ strategies for GTA training and development programs, however, articles are often not supported by empirical research. This article provides a review of empirical research regarding graduate students’ preparation for teaching—first focusing on graduate students in statistics, specifically, and second offering what can be learned from studies of graduate students in other disciplines. We conclude with ten research-based recommendations for preparing graduate students to teach statistics, along with practical ideas for how to implement them.

KEYWORDS:

• Graduate teaching assistant
• Statistics education
• Teacher preparation

1 Introduction

Across the world, graduate students hold various roles related to teaching. In Canada, graduate teaching fellows may have the primary responsibility for designing and administering courses, whereas graduate teaching assistants (GTAs) typically lead tutorials or lab sections, grade assigned work, hold office hours, and monitor course websites (Hoessler 2015). At Lancaster University in the United Kingdom, graduate students may facilitate field work or lead discussion groups (Park and Ramos 2002). For this article, the term GTA will be used to refer to any graduate student who has been hired by their institution to serve as the instructor of record or as an assistant to the instructor of record.

Many statistics departments rely on GTAs to teach courses. For example, in the United States, GTAs teach 25% of introductory statistics courses in Ph.D.-granting statistics departments (Blair, Kirkman, and Maxwell 2013). Due to institutional financial pressures, the use of GTAs will not likely decrease (e.g., Birch and Morgan 2005), and questions arise as to how GTAs can be prepared and supported for teaching.

The literature related to GTAs in statistics is primarily descriptive, sharing innovative ideas about preparing GTAs for teaching (e.g., Rumsey 1998; Garfield and Everson 2009). In a special section of The American Statistician, strategies from four United States statistics departments are highlighted, including courses and weekly meetings (e.g., Birch and Morgan 2005; Gelman 2005; Harkness and Rosenberger 2005), mentoring (Froelich, Duckworth, and Stephenson 2005), and immersion in a departmental culture (Birch and Morgan 2005). As mentioned by Moore (2005), all the featured statistics departments’ strategies appear to encourage teaching that is student-centered (focused upon facilitating conceptual change) as opposed to teacher-centered (focused upon transferring knowledge; e.g., Saroyan, Dagenais, and Zhou 2009). However, little empirical evidence has been collected to study the extent to which various strategies successfully achieve the intended goals.

This article offers a review of empirical research related to the preparation of graduate students to teach statistics. After reviewing studies of GTAs in statistics, we turn briefly to studies of GTAs in other disciplines. In conclusion, ten research-based recommendations for preparing and supporting GTAs as teachers of statistics are offered, as well as practical suggestions for how to implement the recommendations.

2 Studies of GTAs in Statistics

This article focuses on six studies of GTAs in statistics, specifically. The methodologies vary, including large survey studies (e.g., n = 218), or qualitative studies using case studies (e.g., n = 4), or focus groups and interviews (n = 10). All six studies involve GTAs at United States institutions. The authors of all the reports appear to agree that statistics GTAs need improved preparation and support for teaching statistics.

The studies primarily attend to four topics: GTAs’ statistical content knowledge, GTAs’ knowledge for teaching statistics (including both pedagogical and pedagogical content knowledge), GTAs’ beliefs about how statistics should be taught, and GTAs’ preparatory experiences for teaching statistics. Here, we briefly summarize results related to each of these four topics.

2.1 Statistics GTAs’ Content Knowledge

The studies of GTAs in statistics suggest that GTAs may have procedural understanding of statistical topics but are unable to connect their understanding to novel situations. For example, after a survey of 68 GTAs from 18 institutions and five follow-up interviews, Noll (2011) found that many GTAs had knowledge about the statistical theory of sampling, but struggled to connect ideas to empirical or simulation-based applications. In a similar study conducted by one of Noll’s doctoral students, Dolor (2017) examined graduate students’ understanding of p-values using mixed methods (n = 30 survey respondents and four follow-up interviews). Dolor discovered that most participants understood how the magnitude of the p-value can be used to show a statistically discernible (significant) result, however, very few participants were able to coordinate different ways of thinking about p-values (e.g., conditional probabilities, comparing to a level of statistical discernibility (significance), or relating p-values to power).

Results of a large survey study (n = 213 graduate students representing 38 United States Ph.D.-granting institutions) indicated that many GTAs feel they lack knowledge of other important statistical topics (Justice, Zieffler, and Garfield 2017). For example, the majority of participants indicated that they had not learned about nontraditional course topics such as big data or simulation methods for statistical inference.

All of Noll, Dolor, and Justice et al. acknowledge limitations of their volunteer-response surveys. However, their studies provide some clues that there may be many GTAs that are not adequately fluent with sampling distributions, p-values, simulation methods for statistical inference, or other important topics.

2.2 Statistics GTAs’ Pedagogical and Pedagogical Content Knowledge for Teaching

There is also evidence to suggest that GTAs need more opportunities to develop statistical pedagogical content knowledge (see Shulman 1986) and other knowledge for teaching. In the aforementioned survey conducted by Justice, Zieffler, and Garfield (2017, n = 213), most participants indicated they had not learned about recommendations for teaching introductory statistics (e.g., GAISE; ASA 2005) or methods for the active learning strategies endorsed by educational and scientific organizations (e.g., American Association for the Advancement of Science 1989; New Zealand Ministry of Education 2012). Furthermore, the majority of surveyed GTAs indicated they had not learned about research on how students learn statistics (e.g., Garfield and Ben-Zvi 2007).

In a qualitative study of GTAs at a Ph.D.-granting statistics department, Green (2010) found additional evidence to suggest that GTAs need more pedagogical preparation. Even after attending both institutional and departmental preparatory workshops, the GTAs in her study voiced concerns about their ability to teach their students. The GTAs desired more guidance regarding prioritizing course content, sequencing topics, and using technology to enhance student learning.

2.3 Statistics GTAs’ Beliefs About Teaching Statistics

The third area of research on statistics GTAs examines GTAs’ beliefs about how statistics should be taught. Many participants in the survey by Justice, Zieffler, and Garfield (2017) indicated they hold beliefs that are not aligned with current recommendations for teaching statistics (e.g., see GAISE College Report ASA Revision Committee 2016). For example, there was not clear consensus among participants about the use of active learning strategies to deliver course content. Also, GTAs had mixed opinions about the extent to which students should be required to work in small groups, or required to engage in alternative forms of assessments (e.g., group projects, oral presentations).

In an in-depth case study of n = 4 GTAs, Findley (2019) found clear disconnect between GTAs’ beliefs about statistics and their teaching practices. Based on data collected from teaching observations, teaching artifacts, and written reflections about teaching, his analysis revealed that even GTAs who viewed the discipline of statistics as flexible, contextually driven, and without black-and-white answers posed to their students tasks that reflected none of these characteristics. The GTAs tended to defer instead to computationally driven pursuits of “the right answer.”

In another recent survey study of n = 218 graduate students in statistics and biostatistics departments, Justice (2017) explored the extent to which participants’ beliefs about various aspects of teaching statistics were student-centered. By way of retrospective (then vs. now; looking back) pretests (Bray and Howard 1980), Justice investigated current beliefs and compared them to GTAs’ perceived beliefs prior to entering their degree programs. Responses suggested that GTAs tend to judge their own beliefs to have become more student-centered. For example, GTAs tended to favor more class-time spent on students communicating their ideas in small groups, and less time conducting lectures or demonstrations. GTAs also generally opted for more frequent use of simulation methods to teach statistical inference, and more assessment items that require students to provide explanations of their reasoning using words. These results indicate that GTAs’ beliefs about teaching statistics may be able to change during the course of their graduate studies, and that on average, the change is toward more student-centered teaching pedagogies.

2.4 Statistics GTAs’ Preparatory Experiences

The fourth and final line of research regarding statistics GTAs examines how GTAs are prepared for teaching. The survey results by Justice, Zieffler, and Garfield (2017; n = 217) suggest the most frequent type of preparation was observations with feedback; about half of participants indicated they had experienced an observation of their teaching with feedback. The survey did not inquire whether the observation was conducted by a statistics faculty member, a peer GTA, or other university personnel. The next three most frequent types of preparatory experiences were summer or semester-long courses (44%), faculty mentors (40%), and 1–2 day workshops (40%). The natures of the courses, mentoring relationships, and workshops were not explored in this study.

There is strong evidence that an important part of GTAs’ preparatory experience is their interactions with each other. Green (2010) found that GTAs tended to share strategies for teaching with each other and rely on each other for support. In particular, the more experienced GTAs in the program provided support for the novice GTAs. To further explore GTAs’ support for each other, Justice (2017) examined the extent to which graduate students appear to engage with each other in formal and informal conversations related to teaching. Over 40% of participating graduate students indicated that they attend required meetings about teaching topics at least as often as twice a month. Roughly half of the participants indicated that they engage in voluntary discussions related to teaching at least twice a month, often without a faculty member present. These results are consistent with overwhelmingly strong evidence that GTAs in all disciplines help prepare each other for their teaching roles and rely heavily on each other for support (e.g., Darling 1987; Darling and Staton 1989; Staton and Darling 1989; Williams and Roach 1992; Jones 1993; Myers 1994, 1998; Austin 2002; Wulff et al. 2004).

2.5 Summary of Research on Statistics GTAs

The current research is not strong enough to paint a crystal-clear picture of the knowledge, beliefs, and preparation that GTAs have for teaching statistics. All the studies reviewed above were likely to recruit study participants interested in topics related to teaching and learning, and small sample sizes limit the ability to assess the psychometric properties of the instruments used in the surveys. Furthermore, all the studies were conducted in the United States, and questions remain about statistics GTAs in other countries.

Yet these studies provide a rough sketch of the nature and scope of GTA preparation in one part of the world. There appears to be consensus that many GTAs in statistics departments need more knowledge, preparation, and support as they fulfill their teaching roles. But what strategies should be used to prepare GTAs? What support actually works? And how can departments provide support within the confines of their limited time and resources? For answers to these questions we turn to research on GTAs in other disciplines.

3 GTAs in Other Disciplines

The challenge of GTA preparation for teaching is certainly not specific to statistics. GTAs are used for other disciplines, including those that “house” statistics courses applied to their discipline (e.g., economics, mathematics, psychology). Although this article focusses primarily on studies of statistics GTAs, here we provide a brief review of literature regarding GTAs in other disciplines. Even when considering the distinctive nature of statistics as a discipline (e.g., Cobb and Moore 1997), there is much to be learned from studies of GTAs in other fields.

Large-scale survey studies indicate that GTAs (and their students!) from a wide variety of disciplines have concerns related to their preparation and support for teaching (e.g., Diamond and Gray 1987; Golde and Dore 2001; Roehrig et al. 2003; Kendall and Schussler 2012). For example, in a survey of over 30,000 GTAs across many disciplines, 45% of participants felt they had received insufficient training for teaching, and nearly half of respondents indicated they lacked faculty supervision designed to improve their teaching (Fagen and Suedkamp Wells 2004).

From what has been written about GTA preparation for teaching, it is evident that there is great variation in the nature and extent of programs offered. Programs vary in length, GTA participation expectations (optional or required), and curricular emphasis (Parrett 1987). Some programs are university-wide (e.g., Wulff, Nyquist, and Abbott 1991); others are discipline-specific (e.g., Speer 2004). Programs may have several components, often including: discussion of readings about how students learn; experiences with active learning; observations of GTAs via practice teaching sessions; discussion of diverse student populations; and ideas for developing inclusive classrooms.

In a review of literature in GTA training, Carroll (1980) called for more empirical research on the effects of training programs rather than simple sharing of innovative ideas. Years later, reviews by Parrett (1987) and Abbott, Wulff, and Szego (1989) echoed Carroll’s call for data-supported research. Today, there are still relatively few empirical studies, and many studies have methodological concerns (e.g., no control group; instruments with no validity evidence; studies that are too short-term to discern potential effect; Wyse 2010).

One common methodological issue is that when a control group is present, the treatment is often an entire preparation program with many components bundled together (e.g., microteaching sessions; discussion of readings, etc.; e.g., Boman 2013). The bundling of experiences in one program makes it difficult to discern the key components of the program (or interactions of several components). A few studies have been able to dissect the bundles and explore specific components of training programs. Two components that appear particularly promising are teaching observations and mentoring.

3.1 Teaching Observations

Teaching observations may take place during regular class sessions (in-person or using video recordings) or using microteaching sessions, which are short, practice-teaching simulations performed for peers and situated outside of regular class. Teaching observations are usually coupled with follow-up consultations when the observer provides feedback to the observed teacher. GTAs have been found to value observations more than other training program components (e.g., Dalgaard 1982).

There is strong evidence to suggest that teaching observations may be a key component for improving teaching behaviors (e.g., Hendricson et al. 1980) and teaching affect (i.e., attitudes and values about teaching). In a controlled randomized study, Bray and Howard (1980) found statistically discernible (significant) improvement in teaching behaviors and attitudes toward teaching for GTAs who received consultations regarding video of their teaching (p < 0.001). It is interesting that statistically discernible differences were not found between the GTAs who received video consultations (only) and those who had video consultations in addition to other training components such as seminars and student evaluation consultations (p = 0.6). The authors conclude that the video consultation was the most effective component of the training program.

In a controlled study of 27 GTAs in English departments, Williams (1991) found that a training program reduced GTAs’ anxiety only when coupled with teaching observations and peer GTA mentoring. GTAs experiencing the training program without the observation and mentoring components did not show statistically discernible reduction in anxiety. It is important to note that the observers in the Williams study were not faculty members, but rather senior GTAs. This suggests that there is promise in utilizing senior GTAs to help mentor new novice GTAs (and it is not all dependent on faculty who may already be overcommitted)!

3.2 Mentoring

Studies suggest that mentoring is one way that GTAs can be affected to have more student-centered teaching beliefs and practices as well as improved GTA teaching affect. In a survey of over 60 GTAs from STEM disciplines, Gilmore et al. (2013) studied correlations between GTAs’ beliefs about teaching and four factors: experiences being mentored, teaching experience, research experience, and training program experience. They found that mentoring—more so than the other three factors—was predictive of the extent to which GTAs’ teaching beliefs were student-centered.

There is more evidence to suggest that mentoring can serve as an effective strategy. A case study by Volkmann and Zgagacz (2004) recorded dynamic changes in a physics GTA’s teaching beliefs and teaching practices while engaging in a mentoring relationship. In the aforementioned study by Williams (1991), peer GTA mentoring was one of the two key components necessary for a training program to show discernible (significant) reduction in anxiety. Mentoring has also been employed by the Preparing Future Faculty (PFF) program, which has been cited as “one of the most systematic efforts to increase graduate student preparation for teaching” (Pruitt-Logan and Gaff 2004). Former president of the American Statistical Association, Robert Hogg, once stated, “it is clear that all of us would profit more if professors would serve as mentors to graduate students in teaching as well as research” (Hogg 1991, p. 343). Mentoring has been rated by GTAs as very helpful (e.g., Jones 1993).

Although faculty often serve as mentors (e.g., Huang, Strawderman, and Usher 2013), it is best to think more broadly about what mentoring may look like. The mentors in the Williams (1991) study were senior GTAs. There is evidence that peer GTAs can—and do—mentor one another. When acknowledging the network of mentors that GTAs tend to create for themselves, it is appropriate to consider a community of practice approach to GTA preparation for teaching.

3.3 Participation in a Community of Practice

The term “communities of practice” was coined by Lave and Wenger (1991) when they set out to study apprenticeship models in various workplaces and organizations across the world. Lave and Wenger were surprised to find that healthy apprenticeships often tend to involve an entire community of novices and experts engaging together, rather than individual pairs of mentors and mentees. Communities of practice can be defined as groups of practitioners who deepen their knowledge and expertise by interacting with each other on an ongoing basis.

Communities of practice have been found to serve as an asset to businesses and organizations. For example, participation in communities of practice can keep experts interested and at the cutting edge of the practice (Wenger, McDermott, and Snyder 2002). The communities can steward valuable knowledge and, under certain conditions, can pass the knowledge on to newcomers. Unfortunately, communities of practice are not always benevolent to their host organizations (e.g., Lave and Wenger 1991; Wenger, McDermott, and Snyder 2002; Schlager and Fusco 2003). For example, communities of practice can be closed to new ideas, or they can promote mediocrity.

There are many ways that GTAs may participate in communities of practice related to teaching, including observations with feedback, mentoring, attendance and engagement in weekly meetings, or even spontaneous interactions such as casual conversations in a shared office. For example, it may be considered participation in a community of practice when a GTA strikes up a conversation with a peer regarding something they overheard that peer say to a student during office hours. Some communities of practice engage only informally and go unrecognized by their host institutions (Schlager and Fusco 2003).

There is overwhelming evidence to suggest that it is important to GTAs to participate in a healthy community of practice (Darling 1987; Darling and Staton 1989; Staton and Darling 1989; Williams and Roach 1992; Jones 1993; Myers 1994, 1998; Austin 2002; Wulff et al. 2004; Crede, Borrego, and McNair 2010; Green 2010). This large body of evidence suggests that GTAs primarily look to one another to seek information regarding their teaching responsibilities. Let it be emphasized: research suggests GTAs tend to consider each other to be more helpful than any of faculty, workshops, courses, or other sources of professional development that a department may provide to try to inform their teaching. In addition, GTAs have been found to be the strongest influence on each other. Moreover, those GTAs that do participate in a community of practice often voice that they desire more interactions with one another (e.g., Crede, Borrego, and McNair 2010). This body of evidence suggests that the community surrounding GTAs is critically important to their professional development.

Those who seek to prepare GTAs for teaching but opt to ignore the communities of practice housed within their departments may be providing preparatory experiences in vain. To think of GTA professional development as a series of courses, workshops, observations, and/or mentoring opportunities is to miss the mark; the evidence suggests that what is most influential on the GTAs’ professional development as teachers is the entire community of practice surrounding the GTAs. On the other hand, departments that view GTA professional development as a series of courses, workshops, observations, and/or mentoring opportunities designed to engage with, cultivate, and shape the GTAs’ community will have more success. These departments will acknowledge that it is the entire experience and the entire community (not a series of interventions) that influence the GTAs’ growth.

3.4 A Note About International GTAs

Before turning to recommendations for statistics GTA preparation, we turn briefly to the historically hot-topic of international GTA preparation for teaching. Much has been written regarding concerns about the preparation of foreign GTAs to teach in their nonnative countries (e.g., Byrd, Constantinides, and Pennington 1989). In fact, concern was so widespread in the 1980s that there emerged the controversial phrase “the foreign TA problem” (Fisher 1985). As a response, some state legislatures mandated screening of international GTAs for language proficiency (Thomas and Monoson 1993). Such screenings have been criticized, and appropriately so; research studies suggest other variables such as softer accent and—interestingly—culturally sensitive teaching styles are more relevant to GTA teaching success (Bailey 1983; Jacobs and Friedman 1988; Hoekje and Williams 1992; Rubin 1992; Luo, Grady, and Bellows 2001). For example, international GTAs with high English proficiency have received worse student ratings than GTAs with lower proficiency but teaching styles that are more typical of the culture surrounding the institution.

Based on this research, experts agree that international GTA development programs ought to include cultural issues, such as the departure from authoritarian teaching styles (Fisher 1985; Constantinides 1987, 1989; Travers 1989; Weimer, Svinicki, and Bauer 1989; Davis 1991; Gilreath and Slater 1994; Sarkisian and Maurer 1998). Some examples of how cultural issues may be introduced include demonstrations and video showings of active learning sessions, followed by personal reflection and discussion.

4 Ten Recommendations for Statistics GTA Professional Development for Teaching

Based on empirical research reviewed, this article offers ten recommendations for GTA professional development programs for teaching statistics. The recommendations can be categorized in three broad themes: (A) cultivate an interactive community of novices and experts; (B) challenge GTAs’ teaching beliefs and practices; and (C) develop GTAs’ knowledge for teaching statistics. The recommendations are given in Table 1. It is important to note that the themes are not mutually exclusive; some recommendations may fall under more than one theme. For example, reading and discussion about how students learn statistics (Recommendation 7) may challenge GTAs’ teaching beliefs and practices (Theme B) as it develops GTAs’ knowledge for teaching (Theme C). Elaboration of each recommendation and supporting examples and research citations are given in the subsections that follow.

Table 1 Ten research-based recommendations for statistics GTA professional development for teaching, grouped by theme.

Number	Recommendation
	Theme A: Cultivate an interactive community of practice engaging all levels of expertise (e.g., novices with experts, novices with junior experts, novices with novices, etc.)
1.	Assign GTAs to increasingly legitimate peripheral participation.^a
2.	Establish formal interactions (e.g., observations with feedback, mentoring relationships, weekly meetings).
3.	Provide opportunities for informal interaction (e.g., shared spaces, informal gatherings).
Theme B: Challenge GTAs’ teaching beliefs and practices
4.	Model a variety of interactive pedagogical methods appropriate for the student audience.
5.	Observe GTAs teaching and provide feedback.
6.	Encourage habitual reflection upon teaching for the purposes of self-evaluation.
Theme C: Develop GTAs’ knowledge for teaching statistics
7.	Provide opportunities to develop pedagogical knowledge for teaching statistics.
8.	Guide GTAs about how to use technology to enhance course content.
9.	Provide opportunities to develop content knowledge for teaching statistics including topics such as simulation methods for statistical inference.
10.	Provide curriculum and assessment resources for GTAs to use as a reference.

a NOTE: Legitimate peripheral participation is described in detail by Lave and Wenger (1991) in their book, Situated Learning: Legitimate Peripheral Participation. In this context, (briefly): legitimate peripheral participation involves opportunities for GTAs to participate authentically in the practice of teaching. These opportunities would change in nature as the GTA moves from a newcomer to an expert, progressively moving toward taking on tasks and roles more central to the practice.

4.1 Theme A (Recommendations 1–3): Cultivate an Interactive Community of Novices and Experts

The three recommendations in Theme A involve cultivating a community of novices and experts who interact regularly; in short, to foster a community of practice. Overwhelmingly throughout the literature there is evidence that GTAs need support from each other and from faculty (e.g., Staton and Darling 1989; Jones 1993; Myers 1994; Luft et al. 2004; Green 2010). The term “cultivate” is used because healthy communities of practice generally cannot be forced; they can only be given the ripe conditions for healthy growth (Wenger, McDermott, and Snyder 2002).

The community of practice approach to professional development shifts away from a psychological view of learning (namely, learning occurs when someone’s understanding and conceptions are refined). Instead, learning is viewed as engaging in more central tasks to the practice, called legitimate peripheral participation (Lave and Wenger 1991). In our context of GTA professional development, a GTA’s learning may be indicated by their roles changing from more peripheral—albeit legitimate—participation (such as grading papers or holding office hours) to tasks more central to teaching (such as creating assessments or designing and administering lessons).

It follows that Recommendation 1 is to appropriately assign GTAs to progress in increasingly more legitimate peripheral participation (Nyquist and Sprague 1998; Luft et al. 2004). The speed of progression may vary from GTA to GTA, but the tasks must always be legitimate, progressively growing to be more central to the practice of teaching. Tasks to consider (in addition to the aforementioned tasks of grading papers, conducting office hours, creating assessments, and designing and creating lessons) may include creating and administering mini-lessons, preparing short presentations with feedback regarding assessments the GTAs have recently graded, conducting peer observations with feedback, designing and running workshops to prepare newcomer GTAs, compiling a resource library for newcomer GTAs, or being involved with textbook selection and/or curriculum redesign. A nice example of a department of engineering that implemented this recommendation is outlined by Crede, Borrego, and McNair (2010). Sprague and Nyquist (1989) offered suggestions for how to discern whether GTAs are ready to take on more responsibility, such as noticing how the GTAs talk about their discipline or how they relate to authority.

Regardless of the extent of GTAs’ responsibilities, it is important to clearly specify the responsibilities and monitor GTAs’ progress (Jones 1993; Wulff et al. 2004; Green 2010). Lack of clearly outlined expectations and absence of faculty feedback are primary complaints among GTAs across all disciplines regarding their experiences as instructors and teaching assistants (e.g., Williams and Roach 1992; Jones 1993).

Recommendation 2, which has the very strongest research-base, is to provide more formal interaction between novices and experts: namely, mentoring and teaching observations with feedback (e.g., Williams 1991; Jones 1993; Volkmann and Zgagacz 2004; Green 2010). These opportunities need not be dependent on faculty; senior and peer GTAs may be able to mentor each other (e.g., Darling 1987; Williams 1991) or conduct the teaching observations. If a department would like to encourage GTAs to mentor each other, the faculty may need to help GTAs learn how to do so appropriately and effectively. A helpful article describing the evolution of a mathematics department’s peer-observation activities is given by Speer (2004).

Other ways to encourage more formal interactions between novices, their peers, and experts, is to hold regular meetings for faculty, senior GTAs, and novice GTAs to discuss their teaching responsibilities and experiences. A fine example of a statistics department’s approach to these meetings is given by Rumsey (1998). Again, it is an open question as to whether faculty need to be present at the meetings, or whether senior (or peer) GTAs can facilitate.

Recommendation 3 is to find ways to build the community of practice by encouraging informal interaction between faculty (experts), senior GTAs (junior-experts), and novice GTAs (Darling 1987; Staton and Darling 1989; Williams and Roach 1992; Luft et al. 2004; Moore 2005; Green 2010). Examples include devoting a lounge, shared office, or a space where GTAs are welcome to commune; providing food and refreshment to encourage social and professional interaction; hosting events with discussion before or after, and rewarding healthy behaviors with recognition, awards, or other incentives (Wenger, McDermott, and Snyder 2002).

4.2 Theme B (Recommendations 4–6): Challenge GTAs’ Teaching Beliefs and Practices

Theme B involves challenging GTAs’ teaching beliefs and teaching practices. This theme is certainly not mutually exclusive from Theme A; these recommendations may also be embodied as a part of engaging in a community of practice related to teaching.

Recommendation 4 is to model the pedagogies that are desired for GTAs to implement. GTAs’ teaching beliefs and teaching practices can be challenged through observing faculty who model the desired approaches (Gelman 2005; Volkmann and Zgagacz 2004; Moore 2005). This may be especially important for international GTAs to learn about the culture of teaching in new countries (Hoekje and Williams 1992). After GTAs observe new teaching practices, they may need to engage in follow-up discussion and reflection upon the methods used (e.g., Volkmann and Zgagacz 2004).

Recommendation 5 reiterates the importance of conducting observations and providing feedback (Recommendation 4; Bray and Howard 1980; Abbott, Wulff, and Szego 1989; Gilreath and Slater 1994; Belnap 2005; Moore 2005; Justice, Zieffler, and Garfield 2017). To be clear: feedback should be provided to the GTA after every observation. The observations can come in many forms: microteaching simulations during a workshop or course on teaching, or live teaching sessions with “real” students. Faculty, senior GTAs, or peer GTAs can conduct teaching observations. If GTAs are conducting observations of each other, there is some evidence that both parties will get more out of the experience if they are provided with guidance (e.g., Speer 2004).

GTAs who are assigned even minimalist tasks can benefit from observations and feedback. For example, a GTA who holds office hours can be observed for a few moments and provided feedback on the extent to which they built on students’ ideas or gave students wait time to think and respond to questions.

Recommendation 6 is to encourage GTAs to develop a habit of reflection upon their own teaching (Constantinides 1987; Luo, Grady, and Bellows 2001; Schussler et al. 2008; Kendall and Schussler 2012). Self-reflection activities may help GTAs develop awareness of issues in racial, cultural, and ethnic diversity (e.g., Zeichner 1987; Gay and Kirkland 2003). Reflection may be particularly important for international GTAs, helping them identify their own personal teaching style, and comparing it to the culture of their current institutions.

4.3 Theme C (Recommendations 7–10): Develop GTAs’ Knowledge for Teaching Statistics

Theme C includes recommendations focused on developing GTAs’ knowledge for teaching statistics. Knowledge for teaching statistics includes pedagogical knowledge, pedagogical content knowledge, and content knowledge (Shulman 1986). As with before, these recommendations are not exclusive of the previous two themes; GTAs who learn about how to teach statistics (Theme C) may change their beliefs and teaching practices in response (Theme B). They also may engage in a community of practice differently (Theme A) based on their new knowledge, and so on.

Recommendation 7 is to provide opportunities to develop research-based pedagogical knowledge for teaching statistics. This recommendation is based on the aforementioned studies conducted by Green (2010), Justice, Zieffler, and Garfield (2017), Noll (2011), and recommendations by Rumsey (1998), all of which suggest that statistics GTAs need more opportunities to develop knowledge needed for teaching statistics. One method for developing this knowledge may be to read and discuss the growing literature on how students learn statistics. It is important to note that while research on common misconceptions may be relevant and very popular (e.g., Tversky and Kahneman 1974), GTAs should also read and discuss research on how students learn statistics (e.g., Garfield and Ben-Zvi 2007), the latter of which is often overlooked in statistics GTAs’ preparation (Justice, Zieffler, and Garfield 2017). GTAs should be exposed to the Statistics Education Research Journal (SERJ), a peer-reviewed online journal that is freely available from the International Association of Statistics Education (https://iase-web.org/Publications.php?p=SERJ). GTAs may also need help with the selection and ordering of topics (e.g., Green 2010) and other pedagogical or pedagogical content knowledge.

Recommendation 8 is designed to highlight a particular type of pedagogical content knowledge for teaching statistics, namely technological pedagogical content knowledge (e.g., Golde and Dore 2001; Lee and Hollebrands 2008; Green 2010). A GTA who is comfortable using technology to analyze data may need guidance on how to help students learn to use the technology to do the same thing. Also, GTAs may need guidance using technology designed for teaching statistical concepts (e.g., TinkerplotsTM software, Konold and Miller 2015; Introduction to Statistical Investigations (ISI) Applet Collection, http://www.math.hope.edu/isi/applets.html), especially if they are not familiar with the simulation-based methods these technologies are designed to illustrate. A journal that provides many resources related to statistics education technology is Technology Innovations in Statistics Education (TISE), which is freely available online (https://escholarship.org/uc/uclastat_cts_tise).

To supplement knowledge for teaching statistics, Recommendation 9 is to provide opportunities for GTAs to develop knowledge about statistics itself. Topics such as simulation methods for statistical inference, empirical sampling distributions, and connections between aspects of p-values may provide an excellent start (Noll 2011; Dolor 2017; Justice, Zieffler, and Garfield 2017), although there is still room for more research on how to help GTAs develop understanding of these content areas.

The final recommendation is to provide curriculum and assessment resources for GTAs to use as a reference (Recommendation 10; Rumsey 1998; Moore 2005). One great resource is the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE) website, which freely provides literature, webinars, and other resources (https://www.causeweb.org/cause/). GTAs can subscribe to the causeweb listserv and be notified of conferences and other news in statistics education.

Resources to introduce to GTAs may also include assessment tools. GTAs can find test items and other assessment resources on the Assessment Resource Tools for Improving Statistical Thinking (ARTIST) website (https://apps3.cehd.umn.edu/artist/). On the ARTIST website GTAs can sign up for students to take the CAOS assessment (delMas et al. 2007). Several more statistics assessments are on the International Association for Statistics Education list of doctoral dissertations in statistics education (https://iase-web.org/Publications.php?p=Dissertations; e.g., Zeigler 2014; Beckman 2015; Sabbag Sabbag 2016; Le 2017).

5 Implementing the Recommendations: Practical First-Steps

There are many practical steps that may be feasible for a department with limited resources. If GTAs do not experience many observations of their teaching, consider asking faculty to observe for just a part of a class period instead of feeling obligated to observe for the whole class session. If the institution has a center for teaching and learning, considerer soliciting observation services from them. Finally, consider empowering senior GTAs to conduct observations (Williams 1991), perhaps in exchange for a small stipend or another helpful incentive (e.g., improved office space; a teaching mentor award, etc.). Be sure to provide some guidance as to what senior GTAs may look for and how they can provide helpful feedback (e.g., Speer 2004).

If mentoring is too time-consuming for faculty, senior GTAs may be solicited to serve as mentors to novices. In addition to class observations, the senior GTAs could meet with GTAs regularly and share resources they have used. Perhaps the department could fund a tuition waiver or stipend for a senior GTA in exchange for their services. (This may be cheaper than hiring a faculty or full-time instructor to do so). An example of a statistics department that has made extensive use of senior GTAs to help train novices is given in a webinar by Schwab and Blankenship (2014) from the University of Nebraska.

Senior GTAs may be able to take steps to cultivate a whole community of practice. They may be able to plan and run preparatory workshops, facilitate weekly meetings, and mentor novice GTAs. A senior GTA may be charged with facilitating discussion after a group-showing of a CAUSE webinar on a topic of interest. Two examples of GTA communities of practice in other STEM disciplines are given by Holmes et al. (2013), and Crede, Borrego, and McNair (2010).

There are other steps that can be taken to foster community among GTAs. According to Wenger, McDermott, and Snyder (2002), communities of practice may thrive if they are given a desirable common shared space. For GTAs, providing a shared office may help encourage spontaneous conversations about teaching strategies. If the office can be locked GTAs may be more likely to make it a second home, keeping books and materials there. If there is a way to shut the door and chat privately they may be able to have authentic conversations with each other without students within earshot. Food, comfortable seating, fridges, and microwaves may encourage use of the space.

For departments that do not wish to reinvent an entire course on GTA preparation, or that feel uncertain about how such a course could be taught, it may be helpful to know that the course Garfield and Everson (2009) described has since been taught by a number of instructors across the country with various levels of collaboration, including shared guest speakers and discussions via virtual meetings. A department wishing to start a course with support may wish to contact the author to get connected with some of these collaboratively minded groups, perhaps beginning with a 1-credit seminar-type course that simply meets to listen, discuss, and reflect.

6 Future Directions

There are still open questions as to how to implement the ten research-based recommendations given above. For example, research could be conducted to examine what a senior-to-novice GTA mentoring relationship may look like, what scaffolding senior statistics GTAs need to conduct an effective observation, or what makes a shared space ripe for a healthy community of practice related to teaching statistics. Questions remain as to how GTAs may be able to effectively facilitate their own weekly meetings, and if so what the faculty can do to support them. Also, there are many questions regarding the extent to which the studies reviewed here, which largely represent the United States, generalize to other countries and academic cultures. Some work is already underway exploring other questions related to statistics GTA preparation for teaching (e.g., Kaplan and Roland 2018).

In addition to the research that must be conducted, there is a need for changes in the structure of GTA development. As it stands, institutions have little incentive to invest in GTAs that will graduate and serve as professors at competing institutions. Meanwhile, aside from personal motivation, GTAs often have little incentive to grow as teachers in a culture that typically prioritizes research over teaching (e.g., Boyer 1990).

There is a need for help from professional associations, government agencies, and other parties that may bring funding and prestige to GTA development efforts. Inter-institutional teaching communities of practice, graduate-student teacher development awards and scholarships, and other innovative strategies may be able to help prepare GTAs to facilitate student learning and develop a statistically literate society.

The challenges and strategies presented here may not be specific to GTAs. Like GTAs, faculty can hold teaching beliefs and teaching practices that are resilient to change. As they face unprecedented challenges (and opportunities) for their teaching (e.g., socially distanced teaching during a pandemic; raising issues of racial injustice during the Black Lives Matter movement), expert faculty members may be more open to legitimate peripheral participation in a community of practice. Cultivating communities of practice in these challenging contexts may not be easy; just as with teaching, they may require creativity, innovation, and flexibility.

Acknowledgments

Special thanks to Joan Garfield and Andrew Zieffler for their guidance on this project, and to L.L.C. for her proofreading and writing suggestions.

Additional information

Funding

The research presented in this article was supported by the National Science Foundation (NSF CCLI ASA-0206571).