Preparing facilitators to use and adapt mathematics professional development materials productively

Facilitating professional development

Professional development (PD) for mathematics teachers is central to efforts to improve classroom instruction and student learning, both in the USA and internationally. Building on classroom research that highlights the interaction between the curricular materials, teachers, students, and the local context (Ball and Cohen 1996; Cohen et al. 2003), PD has correspondingly been described as consisting of four key elements: the professional development program, teacher participants, the facilitator, and the local context (Borko 2004; Knapp 2003; see Fig. 1). Unpacking the interactive and reciprocal relationships between these elements allows us to better understand how particular PD programs work and what makes them more or less effective with respect to their learning goals.

Important research has been conducted on what leaders of mathematics PD need to know and do to be effective facilitators (Elliott et al. 2009; Le Fevre 2004). For example, Carroll and Mumme (2007) proposed that facilitators should be equipped with detailed knowledge of the subject matter, information about the teachers they will be working with as well as the students of those teachers, knowledge of teaching both children and adults, and knowledge of how to use the PD materials to create a productive learning environment. Borko et al. (2011b) suggested that leaders of mathematics PD need to be especially well versed in three central facilitation practices: (1) engaging teachers in productive mathematical work, (2) leading discussions about student reasoning and instructional practices, and (3) building a professional learning community.

Other researchers have documented specific facilitation moves that contribute to the effective use of video-based PD programs. In such programs, conversations around the video are considered central to deepening teachers’ noticing and analysis of critical issues related to mathematics teaching and learning, ideally leading to more reflective classroom practice (Sherin and van Es 2005; Star and Strickland 2008; van Es and Sherin 2010). A number of researchers are beginning to offer frameworks to characterize the skillful facilitation of video-based discussions in PD workshops (Zhang et al. 2011; Borko et al. 2014a, b; van Es et al. 2014). For example, van Es et al. (2014) identified facilitation practices that engage mathematics teachers in substantive talk about video. First, effective facilitators orient their participants to the video analysis task at hand, for example by asking questions that enable teachers to readily enter into the conversation. Then, successful facilitators maintain both an inquiry stance and a focus on connection between the video and the mathematics content. Lastly, expert facilitators ensure that the discussion is a collaborative effort in which all participants are engaged and offer a variety of perspectives.

Facilitating highly specified PD programs

PD programs vary according to their focus, duration, goals, and resources, among other things. Previously, we have argued that PD programs can be understood as falling on a continuum from highly adaptive to highly specified (Borko et al. 2011a; Koellner and Jacobs 2015). The degree to which programs are adaptive or specified offers some general insights regarding their expected facilitation. Highly adaptive programs are designed to be readily responsive or adapted to the local context. Facilitators are likely to have a relatively strong voice in setting the broad components of adaptive PD, including determining the activities that teachers will engage in and defining the structure of their engagement. By contrast, highly specified programs are intended to support a particular learning environment with predetermined goals, activities, and resources. Facilitators of highly specified PD programs are less likely to select activities; rather, they must become familiar with the tasks and structures provided by the PD.

Successful PD programs include enough flexibility so that they are relevant and responsive to the local context, allow key stakeholders to play a role in decision-making, and encourage participants to take ownership of their learning (Coburn 2003; Darling-Hammond and McLaughlin 1995). Facilitators of specified PD programs are further charged with adhering to the specifications and critical features most central to the PD, using the provided resources in the manner intended by the designers, and understanding when and how to make appropriate adaptations.

In research on classroom curriculum there is a distinction between the “formal curriculum,” the “intended curriculum,” and the “enacted curriculum” (Remillard 2005; Tarr et al. 2008). The formal curriculum refers to that written by textbook publishers or outlined in school policies. The intended curriculum refers to teachers’ plans and aims for using the formal curriculum. The enacted curriculum refers to what teachers actually do with the curriculum in the classroom with their students. There is little debate that, as Remillard (2005) put it, teachers are “active users of curriculum materials and shapers of the enacted curriculum” (pg. 215).

Differences between the formal curriculum and the enacted curriculum, in particular, represent the space in which teachers made decisions regarding fidelity and adaptations (Heck et al. 2012). Brown et al. (2009) provided further depth to this line of reasoning about curriculum enactment and fidelity by pointing out that measuring “coverage” of the curriculum is much less relevant to determining fidelity than documenting students’ “opportunities to learn” afforded by the teacher’s enactment relative to the formal or intended curriculum. Extrapolating from curriculum research to the field of PD, opportunities for teachers to learn based on the facilitator’s implementation are at least as important (if not more so) than precise coverage of the given materials.

Fidelity and adaptation

According to O’Donnell’s (2008) review of the literature, although there are multiple definitions of fidelity of implementation, they are generally quite similar. For our purposes, we define fidelity as the degree to which a facilitator maintains the integrity of the “formal” PD program in their implementation (Borko 2004). When using a highly specified PD program, fidelity entails carrying out the PD in a manner that matches the core activities and learning goals as explicated in the existent PD materials and facilitation resources.

There is some debate regarding the relationship between fidelity and adaptations; however, we side with those who argue that adaptations to any PD program will be necessary to accommodate the unique needs and interests of particular groups of participants (Dane and Scheider 1998). In fact, highly specified PD materials can readily support the coexistence of both implementation fidelity and productive adaptations (Seago 2007). By clearly articulating the recommended workshop activities and facilitation strategies, along with the underlying intentions of the PD, highly specified materials enable informed adaptation decisions that are consonant with fidelity to the designers’ intentions. Seago (2007) proposed that PD facilitators’ adaptations can be categorized using a continuum that includes productive adaptations, no impact adaptations, and fatal adaptations. As long as facilitators make implementation decisions that are productive or have no impact on the participants’ intended experience of the PD, their enactment can be described as maintaining fidelity. Only fatal adaptations adversely impact fidelity by seriously undermining the core principles and goals of the PD.

Mumme et al. (2010) further argue that the need for adaptations to PD programs can arise from external constraints, situational factors, or the facilitators’ knowledge or beliefs. Although this research highlights the range of factors that can influence facilitation choices, preparing PD leaders so that they have a strong knowledge base of the critical features of the program can help to ensure that their adaptations are productive and match the vision of the PD developers. Particularly in the case of highly specified materials, facilitators need to have a thorough understanding of the central learning goals in order to make appropriate “in the moment” adaptations when leading activities and conversations. For example, when leading a discussion, facilitators must have the requisite knowledge to direct teachers’ attention to the critical ideas and topics as intended by the activity (Lesseig et al. 2016).

Preparing knowledgeable facilitators

Facilitating professional development is ambitious and challenging work. Facilitators enter this work with a variety of professional backgrounds and a range of experiences supporting student and/or adult learning. Even facilitators who have previously led workshops must become familiar with the characteristics, processes, and intentions inherent to any PD program that is new to them. Borko et al. (2014b) proposed that facilitators of mathematics PD draw on their “mathematical knowledge for professional development” as they lead workshops. Building from Ball et al. (2008) construct of mathematical knowledge for teaching, mathematical knowledge for professional development encompasses the specialized content knowledge and pedagogical content knowledge that is required of PD leaders. Specialized content knowledge, in this case, includes a sophisticated understanding of the mathematical concepts and relationships intended to be covered during the PD. Pedagogical content knowledge includes the ability to engage teachers in purposeful activities and conversations about those mathematical concepts and relationships and to help teachers gain a better understanding of how students are likely to approach related tasks. Additionally, mathematical knowledge for professional development includes an understanding of how to establish and maintain a professional learning community in which teachers work together productively and collaboratively. Overall, as supporters of teacher learning, facilitators must hold a deeper and more sophisticated knowledge base than the adults they work with, just as teachers must hold a deeper and more sophisticated knowledge base relative to their students.

Facilitators’ mathematical knowledge for professional development likely has a strong connection to their ability to enact a given PD program with fidelity. If a facilitator deeply understands the mathematical content, is knowledgeable about how to work with teachers around this content, is familiar with the appropriate use of the PD resources, and understands the distinction between productive and fatal adaptations associated with a particular program, they will be better equipped to lead the PD with integrity to its core goals and intentions (Even 1999; Lesseig et al. 2016; Mumme et al. 2010; Remillard and Geist 2002). Gaining the requisite knowledge to become an effective facilitator is likely to be a relatively lengthy, socially constructed process, involving in-depth study and disciplined inquiry (Elliott et al. 2009; Jenlink and Kinnucan-Welsch 2001). As Zaslavsky and Leikin (2004) argue, the construction of mathematics teacher educator’s knowledge is a complex process that typically involves facilitators interacting and learning from both “educators of teacher educators” and teachers.

Just like classroom teachers, facilitators need focused support prior to using a formal PD program to ensure that they can effectively pursue opportunities to unpack and build on teachers’ ideas in line with the program’s goals (Remillard and Geist 2002). Providing sustained and focused preparatory experiences for facilitators—such as cooperative planning meetings and facilitation rehearsals—helps them become confident, proficient, and flexible in their role and promotes their ability to make skillful facilitation moves as they are leading PD workshops (Borko et al. 2014a; Santagata 2009; Zaslavsky and Leikin 2004).

Even (1999) emphasized the importance of holding frequent planning meetings with facilitators who are learning a new mathematics PD program in order to develop their knowledge, leadership skills, and create a professional reference group. Even argued that such meetings are “crucial to the development of a common vision and a feeling of shared ownership” (pg. 20). Especially when the PD is highly specified, careful study of the provided facilitation resources along with guidance from knowledgeable others is likely to help the novice facilitator develop a detailed understanding of the program and acquire a sense of which aspects of the mathematical and pedagogical storyline should be maintained to ensure productive adaptations that maintain fidelity (Heck et al. 2012).

Based on their efforts to prepare 72 facilitators to lead mathematics PD, Lesseig et al. (2016) developed a set of design principles to guide others engaged in this type of preparatory work. Specifically, they recommend focusing on teacher learning goals, providing opportunities for facilitators to expand their specialized content knowledge, and using video or other artifacts of practice to generate in-depth discussion and reflection. Certainly structured planning meetings of this sort are essential to ensure that facilitators are adequately prepared to effectively lead PD. We propose that opportunities to “practice” facilitation techniques, especially when using a new PD program, are a beneficial next step.

Lampert et al. (Lampert 2010; Lampert et al. 2013) have argued that rehearsals are a particularly powerful tool for the professional preparation of beginning teachers. Engaging in thoughtfully constructed rehearsals can support novice teachers to gain practical experience managing a realistic and intellectually ambitious learning environment. Among other things, rehearsals allow teachers to practice eliciting and responding to students’ ideas in ways that meet defined instructional goals. In addition, feedback and reflection from rehearsals can inform planning strategies and generate new ideas (Horn and Little 2010). Benedict-Chambers (2016) proposed that rehearsals can be utilized to build beginning teachers’ understanding of the complexity of classroom interactions and to help them notice and attend to critical features of instruction. We suggest that these same benefits apply to novice PD facilitators or those learning an innovative PD program. For mathematics PD leaders, participating in one or more rehearsals as part of the preparation process provides an opportunity to gain mathematical knowledge for professional development that can directly impact fidelity and promote productive (or no impact) adaptations.

The Learning and Teaching Geometry PD program

Our paper is based on an efficacy study of the newly developed Learning and Teaching Geometry (LTG) video-based mathematics professional development (Seago et al. 2017), including whether it produces a beneficial impact on teachers’ mathematics knowledge, classroom teaching practices, and their students’ knowledge in the domain of geometry. The LTG PD program supports up to 54 h of guided professional learning for secondary mathematics teachers. The overall goal of the LTG PD is to improve the teaching and learning of mathematical similarity based on geometric transformations, a topic that has taken on increased importance with the U.S. Common Core State Standards for Mathematics (Seago et al. 2013). The materials follow a learning trajectory that is designed to enrich teachers’ mathematical knowledge for teaching as well as their ability to support students’ understanding of congruence and similarity in alignment with the Common Core.

The role of video in the LTG PD

The LTG project used a design research approach to create the video-based in-service PD program. A central focus of the program is on video clips from a wide variety of classroom lessons, intentionally sequenced to follow a mathematical trajectory. In total, the program includes over 50 video clips, selected from real classroom footage of mathematics lessons across the USA. The clips offer a window into a variety of issues related to content, student thinking, and pedagogical moves. By focusing on classroom video that represents a range of grade levels, geographic locations, and student populations, the program provides insight into what an emerging understanding of similarity looks like as well as specific instructional strategies that can foster this understanding (Seago et al. 2010).

In the LTG materials, video viewing is intentionally sequenced such that it occurs between designated activities. This “video in the middle” design means that video is sandwiched between activities such as mathematical problem solving and pedagogical reflection (Seago 2016). These three elements (pre-video activities, video viewing, and post-video activities) taken together comprise a videocase. Although it is situated “in the middle,” the video clip is in fact the primary ingredient in the design, serving as a focal point of the videocase. Once the video clip has been selected, activities are designed around it to ensure that teachers will engage deeply with the targeted mathematics content, instructional components, and/or student thinking depicted in the clip. The activities surrounding the video also serve as transitions to and from other activities (or video cases) within a given PD session.

Typically, before watching the video, teachers work on and discuss the same problem they will see students working on during the video clip. They might make predictions about how students will solve the problem or what mistakes they might make. After watching the video, the teachers consider the mathematical and pedagogical issues that were brought up by the clip and then reflect on how those issues relate to their own classroom instruction. Specifically, they analyze student’s methods and thinking and the mathematical content that emerges within the teacher and student interactions. In addition, they use evidence from the transcripts to back up claims they make. Taken together, placing video “in the middle” of other PD activities promotes conversations about critical issues related to teaching and learning geometry (Seago 2016). In addition, by situating the PD in actual classroom practice, video helps motivate discussions of how teachers can apply their newly gained insights from the PD to make improvements in their own lessons.

Facilitation resources

As a highly specified model of PD, the LTG PD program contains stated learning goals¹, explicit design characteristics, and extensive resources for facilitators. Facilitation resources include a detailed agenda for each workshop session, PowerPoint slides, video clips and transcripts, lesson graphs², mathematical tasks and other handouts, a Field Guide to Geometric Transformations, Congruence, and Similarity, interactive computer applets, embedded assessments, and a comprehensive Facilitator’s Guide. These resources aim to support facilitators in maintaining the intended mathematical and pedagogical storyline of each session while necessarily adapting the materials to unique groups of participants and their learning and working contexts.

Likely the most important LTG PD facilitation resources are the session agendas. These agendas are intended for the facilitators (not the participants) and contain critical information needed to lead a given session. Each agenda lists the main mathematical focuses (e.g., goals) of the session, and for every activity in the session, the agenda includes a detailed description, a suggested time allotment, the necessary materials, guiding questions, and extensive notes (e.g., further description of the purpose, suggestions for carrying out the activity, optional guiding questions, mathematical support, cautionary notes). Having session agendas with predictable structures is intended to support facilitators in using the materials with integrity to the LTG PD goals and principles while also shaping the parameters for both adherence and flexibility.

Demonstrated effectiveness

Preliminary research on the effectiveness of the LTG PD program, which took place concurrent with its development, offers evidence of the promise of the program to impact teacher and student learning. A portion of the LTG PD materials, the Foundation Module, was piloted in eight sites throughout the USA in order to generate both formative and summative evaluation data. Based on data collected from this pilot, the LTG PD program was shown to lead to significant gains in teachers’ geometry content knowledge, along with the knowledge to effectively convey that information in the classroom. On a content knowledge assessment, the treatment teachers demonstrated an average gain of almost 9 percentage points from pretest to posttest, which was significantly higher than the comparison teachers’ average gain of less than 2 percentage points. Similarly, on assessments embedded within the PD that addressed content and pedagogical content knowledge, the treatment teachers significantly improved on five of the six questions, whereas the comparison teachers did not show significant improvement on any question (Seago et al. 2014).

There is also initial evidence that teachers’ engagement in the Foundation Module can lead to significant increases in their students’ knowledge. Specifically, on an assessment closely tied to the mathematics content in the PD materials, the average pretest–posttest gain for students of treatment group teachers was more than 6 percentage points higher than that for students of comparison group teachers (Seago et al. 2014). The demonstrated gains by both teachers and students suggest that the LTG PD program helps to address the pressing need to provide PD opportunities that improve the learning and teaching of mathematics content explicitly targeted by the Common Core State Standards for mathematics (Marrongelle et al. 2013; Sztajn et al. 2012).

The Learning and Teaching Geometry Efficacy Study

The LTG Efficacy Study aims to further explore the effectiveness of the LTG PD program using a randomized, experimental design. The sample is comprised of 108 mathematics teachers (serving grades 6–12) and their students. Approximately half of the teachers were randomly assigned to take part in the LTG PD in the first intervention year and half will take part in the second intervention year. The intervention consists of the entire LTG PD program, including a 1-week summer institute and 4 days of academic year follow-up sessions beginning in Summer 2016.

As a phase two research endeavor, a primary goal of the LTG Efficacy Study’s central goal is to determine whether the PD program can be enacted with integrity in various settings by a facilitator who was not a developer of the materials (Borko 2004). Most commonly efficacy studies examine the degree to which an intervention has the desired effect under ideal circumstances (O’Donnell 2008), such as utilizing a facilitator with extensive content knowledge and training. As previously noted, in an earlier pilot study that took place as the LTG materials were being developed and revised, facilitators with varying backgrounds from across the USA led workshops in eight sites. During observations of these workshops, project staff noticed a large degree of variance in implementation and made note of facilitator knowledge and skills that appeared likely to correspond to higher levels of effectiveness and fidelity. Specifically, facilitators with strong content knowledge and experience leading mathematics PD appeared to be the most successful in terms of both supporting learning and using the materials in a manner consistent with the expectations of the development team. Based on these experiences, Hannah was selected as the facilitator for the LTG Efficacy Study. Hannah had an exceptionally strong background in the mathematics content (including authoring textbooks) along with prior experience designing and delivering PD institutes focused on similar content. However, Hannah had never facilitated using the LTG PD program, nor had she viewed the materials prior to the start of the LTG Efficacy Study. The co-PI’s (i.e., the authors of this paper) worked with Hannah for an extended period of time to prepare her to lead the LTG PD, as described below.

In efficacy studies, it is essential to demonstrate that a facilitator can implement the PD program with fidelity, in order to argue that any demonstrated impact (or lack thereof) is a true reflection of the PD program and cannot be attributed to implementation failure (Carroll et al. 2007; Raudenbush 2007). Therefore, we systemically documented Hannah’s fidelity of implementation as part of the preparation period (during a facilitation rehearsal). In this paper, we describe both the preparation period and Hannah’s fidelity ratings using existing measures of PD implementation fidelity. We build on these experiences to offer some general conclusions and suggestions regarding the preparation of PD facilitators and the measurement of fidelity.