Middle Grades Mathematics Teachers’ Mixed Perceptions of Content-Focused Professional Development

Abstract

The purpose of this study was to understand how and why middle grades mathematics teachers did or did not fully participate in sustained, content-focused professional development. Qualitative data were collected from middle grades teachers who demonstrated varying levels of participation. The teachers identified opportunities to engage in novel ways with mathematics content as effective in improving their own mathematics understanding and, consequently, their own instruction. Participants who were more critical of the professional development felt the mathematics content was often beyond their specific grade-level. Factors identified as affecting teachers’ participation in the training included administrative support and school-related responsibilities. Offering content-focused professional development designed to reflect the structures and characteristics established in research to most effectively provide teachers with needed knowledge and skills was not enough to ensure teacher participation.

Keywords:

• middle grades
• mathematics teachers
• professional development
• situative perspective
• situated learning

Introduction

Current standards for students’ mathematical learning have been developed over the past two decades and are inclusive of both content and practice standards (e.g., National Council of Teachers of Mathematics, 2014; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). To support educators in their implementation of these standards, National Council of Teachers of Mathematics (2014) identified eight effective mathematics teaching practices (e.g., implement tasks that promote reasoning and problem solving). As the expectations for instructional practice have been raised, there is a need for content-focused professional development in which teachers develop related knowledge and skills to support the implementation of these practices in the classroom. To do so, all teachers need to deeply understand the mathematics content they are teaching and how students learn that content (Association of Mathematics Teacher Educators, 2017; Ball, Hill, & Bass, 2005; National Council of Teachers of Mathematics, 2014; Swackhamer, Koellner, Basile, & Kimbrough, 2009).

Characteristics of effective professional development have been identified from the literature (Desimone, 2009; Guskey & Yoon, 2009) and widely endorsed by the field (e.g., Lindmeier et al., 2020; Main & Pendergast, 2015; Richardson, Miller, & Reinhardt, 2019). These trainings are characterized as follows: content-focused, active learning, coherence, collective participation, and duration (Desimone, 2009; Guskey & Yoon, 2009; Wei, Darling-Hammond, Andree, Richardson, & Orphanos, 2009). However, there is also evidence that inclusion of such characteristics in professional development does not ensure mathematics teachers will elect to participate (Desimone, Smith, & Ueno, 2006; Hill, 2009). Without ways to ensure educators attend sustained, content-focused professional development, the intended outcomes of such trainings will remain lost (Desimone et al., 2006).

The purpose of the current study was to understand why some middle grades mathematics teachers participated in sustained, content-focused professional development and why others chose not to participate, or fully participate in such training. Two research questions informed the current study:

1. What were the perceptions of middle grades teachers who did and did not fully participate in a year-long, content-focused professional development regarding the effectiveness of the training?

2. What factors did middle grades teachers consider when deciding to participate or not fully participate in a year-long, content-focused professional development?

Literature Review

Characteristics of Effective Professional Development

The literature highlights common characteristics of professional development that most effectively provide mathematics teachers with the necessary knowledge and skills. These characteristics—identified in seminal and foundational research—include content-focused, active learning, coherence, collective participation, and duration (Desimone, 2009; Garet, Porter, Desimone, Birman, & Yoon, 2001; Guskey & Yoon, 2009; Swackhamer et al., 2009).

Content-focused

Professional development should focus on enhancing teachers’ content knowledge, with flexibility given to teachers on the best way to apply new understanding within their classroom (Garet et al., 2001; Guskey & Yoon, 2009). Hill and Ball (2004) reported that elementary mathematics teachers’ content knowledge improved when provided with significant opportunities to examine the mathematics taught in the classroom followed by ways in which to connect the learned content with teaching practice. In a similar study, middle grades teachers participated in a summer academy in which they completed mathematics courses that were developed to increase both content and pedagogical content knowledge. The study showed middle grades teachers valued an increased content knowledge of the mathematics they teach, as well as an improved self-efficacy for teaching mathematics (Swackhamer et al., 2009). The effectiveness of content-focused professional development is of particular importance as there is evidence that at the conclusion of teacher preparation programs, some preservice teachers have limited conceptual understanding of particular mathematics concepts (e.g., fractions; see Avcu, 2019).

Active learning

Active learning experiences may include opportunities to review and reflect on student thinking, be observed and provided feedback, lead discussions, and adapt experiences to unique classroom situations (Desimone, 2009; Garet et al., 2001). While active learning experiences can take various forms, Guskey and Yoon (2009) found that active learning activities were determined by the specific content involved, the nature of the work, and the context in which that work took place. In one study, elementary teachers engaged with active learning experiences focused on developing teachers’ content knowledge by reflecting on student thinking embedded in practice (Bell, Wilson, Higgins, & McCoach, 2010). Following eight 3-h sessions result indicated a positive correlation between the teachers’ participation in the professional development and gains in their mathematical content knowledge. In a related study, 500 participants received an average of 58.4 hours of training with activities focused on curricular content knowledge and examining student work—both active learning experiences. Gains in the participants’ mathematical knowledge were statistically significant (Copur-Gencturk, Plowman, & Bai, 2019). Likewise, in a study investigating critical features of effective professional development, Main and Pendergast (2015) surveyed 49 principals and teachers after participation in a two-day workshop focused on adolescent learners. Participants responded more positively when they were engaged in meaningful active learning experiences practicing new skills, solving problems, and observing peers modeling new practices.

Coherence

Professional development that has coherence exhibits alignment between the training and the teachers’ own knowledge and beliefs, as well as alignment between the training and curricular goals and reform policies at the school, district, and/or state level (Desimone, 2009; Garet et al., 2001). Professional development characterized as both content-focused and coherent was found to have the greatest impact on enhanced teacher knowledge and conceptions (Garet et al., 2001; Main & Pendergast, 2015). Jacob, Hill, and Corey (2017) also reported on a three-year training focused specifically on mathematical content knowledge and instructional quality; following the training, a limited impact on teachers’ mathematical content knowledge was reported. The researchers hypothesized coherence across the training and district waned significantly in years two and three of the study as leadership changed and the program no longer had administrative support within the district.

Collective participation

Collective participation is described as the degree to which groups of participants teach within the same school or department (Desimone, 2009; Garet et al., 2001). Main and Pendergast (2015) found that collective participation, including peer support and collaboration, provided the opportunity to develop a shared understanding of the skills and concepts specific to the training. Collective participation has also been shown to increase the cohesion of the training as teachers from the same school often share a common professional culture and may teach the same students and share common assessments. Furthermore, teachers from the same school are more likely to develop a common set of skills to be implemented across classrooms within their school (Garet et al., 2001; Main & Pendergast, 2015).

Duration

The duration of the training should consider the number of hours spent in the training (contact hours) as well as the timespan of the training (Garet et al., 2001). Training that included 30 or more hours provided the most significant effects on student achievement, whereas training that included less than 14 hours showed no significant effects (Guskey & Yoon, 2009). The duration of the training was also found to have the greatest influence on the inclusion of effective characteristics, such as the training being content-focused, inclusive of active learning, and coherent (Main & Pendergast, 2017). In evaluating a large-scale professional development program for teacher leaders, it was the time provided for participants to plan and reflect on the learned materials (active learning), with those at their school and region (collective participation), that participants identified as most effective (Main & Pendergast, 2017). In a separate study, Hill and Ball (2004) attributed the impact of the training on teachers’ mathematical content knowledge to the duration—the training spanned from one to three weeks in the summer (ranging from 40 to 120 hours), followed by 80 hours of training during the school year.

Each of the aforementioned characteristics were considered in the design of the professional development experiences offered within this study. A more thorough description of the training is included within the methods section.

Factors Affecting Participation in Professional Development

Although most teachers attend at least 1 day of professional development each year, 74% of these teachers do not attending the hours needed—30 hours or more—to impact their knowledge or skills (Guskey & Yoon, 2009; Rotermund, DeRoche, & Ottem, 2017). More research investigating the factors which contribute to teacher participation in professional development is needed. Upon review of the literature, factors affecting teachers’ participation in professional development can be subdivided into three categories: (1) the structure and content of the professional development, (2) characteristics of the teachers as learners, and (3) school-level characteristics.

Structure and content of the professional development

Alignment between teachers’ goals and the professional development, the rigor of the professional development content, and the times at which the training is offered were all identified aspects of the structure or content of the professional development that impacted teachers’ participation in training (Krille, 2020; Maloney & Konza, 2011; OECD, 2019; Renninger, Cai, Lewis, Adams, & Ernst, 2011). Specific to the alignment between teachers’ goals and the professional development, Renninger et al. (2011) found that teachers’ participation in problem-solving activities within an online training was limited as teachers found ways to access the desired resources without participating in such activities. Although the goal of the online training was to increase teachers’ mathematical knowledge, given all of the teachers identified finding resources as a goal for participation, teachers’ online engagement was limited. In the same study, the rigor of the content within the training was also shown to impact teachers’ participation. Teachers reporting that they had more prior mathematical knowledge commented on the lack of rigor of the problems and minimal discussion of mathematical content were reasons they did not complete the workshop. On the other hand, teachers reporting less prior mathematical knowledge required more support when solving the challenge problems and felt more intimidated responding to the discussions.

Maloney and Konza (2011) identified the time when the professional development was offered as a factor affecting teachers’ participation. Although participants were provided with both administrative support, clear goals of the training, and common opportunities to participate during the school day, participation in the professional development was minimal. One participant stated that with the trainings offered at the end of the day, it was more difficult to find the mental energy to articulate her thoughts and fully engage. Others did not find the training to be a priority and thus were not willing to give up their time to participate.

Characteristics of the teachers as learners

Teachers’ mathematical content knowledge and willingness to share their practice to others were both characteristics of the teachers that impacted teachers’ participation in training. Desimone et al. (2006) found teachers with strong mathematics backgrounds were much more likely to attend sustained, content-focused professional development when compared to those teachers with limited mathematics backgrounds. The researchers also found educators teaching high-poverty, low-performing students were unlikely to attend compared to their peers who taught mixed-ability classes.

Vulnerability required in sharing ones’ teaching practice and knowledge and/or attempting to engage in new teaching practices or learning was also identified as a factor impacting teachers’ participation in professional development (Guskey, 2002; Park & So, 2014). In a study in which teachers would alternate sharing a lesson plan and allowing the other teachers to observe and provide feedback, Park and So (2014) found the vulnerability associated with opening their classrooms was uncomfortable for the participating teachers. Guskey (2002) also identified the act of attempting change in one’s practice or knowledge as a position of vulnerability. Unless teachers are certain they can successfully engage with the practice or content, they will likely be hesitant as to not risk failure.

School-level characteristics

School-level factors affecting participation—including administration, policies, and workload—have been identified throughout the literature (Gumus, 2013; Krille, 2020; Phillips, Desimone, & Smith, 2011; Wan & Lam, 2010). From examining the TALIS data of 2,891 teachers, Gumus (2013) found teachers who worked for more educated principals and principals employing an accountable management style (as opposed to a bureaucratic style) attended more professional development. Phillips et al. (2011) found mathematics teachers who had more authority over school policy were more likely to attend training than those with less influence. Additionally, teachers whose principals were more involved in their professional growth (power) and who had been at the school for more than 3 years (stability) participated in more hours of content-focused professional development than those with less involved and newer principals. Additionally, Wan and Lam (2010) found that if administrators and colleagues were accommodating in reducing the workload of educators (e.g., finding substitutes), teachers were more likely to attend professional development opportunities.

The structures and characteristics of professional development that lead to teacher learning are well understood. However, further study is needed to understand why middle grades teachers do and do not attend sustained, content-focused professional development programs that include these characteristics. As such, understanding middle grades mathematics teachers’ perceptions on content-focused professional development are needed.

Theoretical Framework

Situated Perspective on Teacher Cognition

A situative perspective was used to frame teachers’ perceptions of the content-focused professional development. Putnam and Borko (2000) identified three themes central to this perspective—that cognition is (a) situated, (b) social, and (c) distributed.

Cognition as situated implies learning does not occur absent from the location, context, and method by which the learning occurred; how the learning is situated becomes central to what is learned (Putnam & Borko, 2000). Teachers’ classrooms are powerful contexts to shape and secure one’s learning. So much of what teachers think and do maybe an automatic response in these familiar settings, making them resistant to change. Providing learning opportunities separate from the comfort of the classroom may be necessary for educators to experience learning about mathematics and mathematics teaching in new ways. Putnam and Borko (2000) identified summer workshops as especially effective for prompting teacher learning as they “appear to be particularly powerful settings for teachers to develop new relationships to subject matter and new insights about individual students’ learning” (p. 7).

Cognition as social suggests what is learned is dependent upon interactions with others (Putnam & Borko, 2000). This suggests that when a diverse group of educators collaborate within communities, teachers can learn from one another’s expertise. Putnam and Borko (2000) posited that existing cultures and discourse communities in many schools might not be conducive to critically examining teaching practice. Developing discourse communities beyond the school may prove powerful and facilitate more critical reflection. Further, Putnam and Borko (2000) stated that bringing together university faculty and classroom teachers to form new communities has proven beneficial for both groups of educators.

Cognition as distributed indicates that knowledge is “stretched over,” or distributed among, other individuals and/or artifacts (Putnam & Borko, 2000). Hodgen (2011) stated that teachers’ mathematical knowledge for teaching is much more embedded within the practice—lesson materials, classroom structures, and communities—and, thus, teachers’ mathematical knowledge may be very different when removed from the context of practice. For example, although a mathematics teacher may be knowledgeable about a particular mathematics topic within the context of teaching—accompanied by curricular materials—the same educator may struggle to correctly answer a novel question related to the same topic removed from the context of that lesson.

Method

Context

The Mathematics Partnerships Project (MPP) professional development program began in the fall of 2012 with the purpose of increasing the mathematics content knowledge of local middle grades mathematics teachers working in high-need schools. At the outset of the project, administrator and district commitment was secured to ensure teachers were supported in their participation. Multiple summer and school-year sessions were offered between the fall of 2012 and summer of 2017. The MPP professional development offerings for the 2016–2017 academic year (beginning in the fall of 2016 and ending in summer 2017), which were the subject of the current study, included both content-focused activities meant to provide teachers an opportunity to increase their overall mathematics content knowledge, and curriculum-focused activities meant to provide teachers an opportunity to work through and discuss conceptual challenges within specific units of their grade-level curriculum.

The 2016–2017 MPP offerings were delivered in two separate professional development opportunities. The first, which will be referred to as the school-year PD, included five sessions held throughout the 2016–2017 school year in the months of September, November, January, March, and April. The second opportunity, which will be referred to as the summer PD, included nine sessions held across two weeks during the month of June. The school-year PD only included content-focused activities, whereas the summer PD included both content-focused and curriculum-focused activities. Content-focused activities were facilitated by three mathematics faculty and one secondary mathematics education faculty. Curriculum-focused activities were facilitated by local curriculum trainers who were also middle grades mathematics teachers. Because the curriculum-focused training only occurred during the summer and was not sustained, findings related to the curriculum-focused activities are beyond the scope of this report.

Within the MPP school-year PD and summer PD, content-focused activities were delivered through participation in Math Circles. Math Circles are communities of practice in which learners have the opportunity to engage with rich problem-solving activities that have multiple entry points and are designed for a wide range of learners (National Association of Math Circles, n.d.). The Math Circles format provides participants opportunities to experiment with various problem-solving techniques, articulate and test those conjectures, and present possible solutions to their peers. Through active learning experiences and high levels of engagement with other participants and session leaders, teachers have an opportunity to develop their own mathematical content knowledge and problem-solving abilities. The learning activities related to equations and expressions as identified in the Common Core State Standards for Mathematics (CCSSM), Grades 6 through 8 (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010).

The following provides an example of a Math Circles content-focused activity. To begin, three stations were created, and at each station, an increasing progression of cups were included. The first station included a sequence of cups arranged to represent a linear progression, the second station was a quadratic progression, and the third was cubic—this information was not made known to the participants. Teachers examined the progression at each station to determine what the next set of cups in the sequence would look like and to determine an equation to evaluate the number of cups at any given step n. After everyone was given an opportunity to share their equations, they engaged in a whole-group discussion about how one could derive an expression to determine the number of cups in any given step for each station—linear, quadratic, cubic. Participants were then given more patterns from the Visual Patterns website (http://www.visualpatterns.org) to practice on their own and to implement with their students. This activity was designed to partially address sixth- and seventh-grade CCSSM standards (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) related to Expressions and Equations (EE), specifically, 6-EE2, 6-EE6, and 7-EE4.

Participants

Forty-three middle grades mathematics teachers were invited to participate in both the school-year PD and the summer PD. Twenty-five teachers enrolled in at least one school-year PD session. Twenty-three teachers enrolled in the MPP summer PD and agreed to participate in the current study. Of those that enrolled in the summer PD, 13 of the 23 participants had also enrolled in the school-year PD. The 23 participants were middle grades mathematics teachers in three counties in the southeastern United States and represented 13 different middle schools, eight of which had been identified as high-need schools. High-need schools were identified based on the percentage of students not meeting proficiency levels in mathematics on the ACT Aspire Test, 2013–2014. Across the 13 middle schools, on average, 77.06% of the students were not meeting proficiency levels for mathematics content standards suggesting a deficit in depth of middle grades content knowledge among the teachers. This is further supported by the fact that 19 of the 23 participants did not have a 6–12 secondary mathematics certification, but instead had either an elementary certification or an elementary certification with a middle grades supplement. Across all participating schools, 82% of students were African American, with 11 of the 13 schools being predominantly African American. The 23 participating middle schools’ mathematics teachers represented various grade levels, teacher certifications, and years of teaching experience, and each are displayed in Table 1 and Table 2.

Table 1 Participant Grade-level and Teacher Certification

	Teacher Certification
Grade Level	Elementary Grades	Middle Grades	Secondary Grades	Elementary & Special Ed	Middle & Special Ed	Total
6	7	1	0	1	0	9
7	0	3	2	0	3	8
8	0	4	2	0	0	6
Total	7	8	4	1	3	23

Table 2 Years of Experience Teaching

Teaching Experience	n
0–2 years	3
3–5 years	9
6– 9 years	2
10+ years	9

Participation in the summer PD sessions was strong with all 23 participants attending most or all of the training sessions. The number of school-year PD sessions that participants attended prior to the summer PD showed greater variance; only 9 of the 25 participants attended three or more of the five sessions. School-year PD attendance prior to summer PD participation is displayed in Table 3 and disaggregated by teacher grade level. Teachers who attended during the school-year PD were provided funds for substitute reimbursement. Teachers who maintained full participation throughout the 9 days of summer PD received a 100 USD per day stipend and access to Connected Mathematics Project 3 (CMP3) curriculum resources, which may have impacted participation. The design of the summer PD provided a unique research opportunity as data were also collected from those teachers who were invited, but did not attend the school-year PD.

Table 3 School-year PD Attendance Prior to Summer PD Participation

	Portion of sessions attended
Grade Level	4 or 5 sessions	3 sessions	1 or 2 sessions
6	2	1	6
7	2	0	7
8	2	2	3
Total	6	3	16

Data Collection and Analysis

Data were collected during the summer PD in June 2017. Qualitative data were collected from all 23 participating teachers through open-ended survey questions. Additional qualitative data were collected from 10 randomly selected teachers through two focus-group interviews.

End-of-experience survey

An end-of-experience survey was administered to gather data on participants’ perceptions of their own learning and the effectiveness of specific aspects of the content-based activities (see Appendix A). Two open-ended survey questions asked teachers to identify the most effective and least effective aspects of the content-focused activities. Demographic data were also gathered, including items addressing the type of teaching certification, grade-level taught, and session attendance.

Focus-group interviews

Twelve teachers from the original sample group, of which 10 agreed, were randomly selected to participate in one of two focus-group interviews. The first focus group included four teachers: two teachers who participated in both summer PD and school-year PD, and two teachers who participated in summer PD only. The second focus group included six teachers: four teachers who participated in both summer PD and school-year PD, and two teachers who participated in summer PD only. In the focus-group interviews, the teachers were asked to: (a) identify and discuss the factors they considered when deciding whether or not to participate in the school-year PD and (b) discuss what they perceived as the more effective and less effective aspects of the content-focused activities in the summer PD (see Appendix B).

The focus-group interviews were recorded and transcribed for data analysis; the first author identified units of analysis by topic change. Data from the focus-group interviews were then independently open-coded by two of the researchers (Corbin & Strauss, 2008). Open-codes were used to develop emergent themes with respect to factors impacting participation in professional development and perceptions of content-focused professional development. Each theme was then connected to its corresponding open code/s within the focus-group transcripts. Following, the two researchers met to discuss each unit of coding and their assigned theme; consensus was reached on all themes representing the data. Lastly, the themes that emerged from the focus-group interviews were independently applied to the qualitative survey data responses; each item response was viewed as a single unit of coding. After one or more themes were applied to each unit of coding, the researchers met to compare assigned themes and consensus was again reached in all cases.

Results

Perceived Effectiveness of Content-Focused Professional Development

A majority of teachers identified effective aspects of the content-focused professional development offerings as opportunities for learning mathematics, applications to the classroom, and learning within a community. On the other hand, a small number of teachers also identified opportunities for learning mathematics and applications to the classroom as the least effective aspects of the content-focused professional development. Both findings are discussed in depth. As a reminder, findings specific to content-focused professional development are inclusive of both school-year PD and summer PD.

Opportunities for learning mathematics

Most participants reported experiencing mathematics learning every time they attended the content-focused professional development. This learning was most frequently described through opportunities to engage with challenging mathematics and, subsequently, opportunities to think and reason in ways similar to the district-adopted mathematics curriculum. Many of the participating teachers enjoyed the challenging problems and, as a result, recognized both a need to increase their own content knowledge and that engaging with such problems provided valuable learning opportunities. For example, consider how one participant reflected on working with challenging problems: “When we worked out some of these problems, like man, I haven’t been in high school or college in years … I have an immediate need to increase my math content knowledge” (6th grade teacher, did attend school-year PD). When asked about the most effective aspect of engaging with the Math Circles problems, another participant stated: “It engages me and I learn something new every single time” (6th grade teacher, did not attend school-year PD). Participants also described how these problems provided opportunities to examine the mathematics from multiple perspectives. For example, one participant stated that she had begun to look at problems from the perspective of a mathematician, while another participant elaborated on this idea saying that problems were approached in ways she would have never considered.

Although the content-focused professional development did not correspond directly with the CMP3 curriculum, teachers remarked that the training required them to solve and think through challenging problems in the same manner the CMP3 curriculum requires of their students; one participant stated, “… the thinking process is still at the core of what happens with CMP, just a way of thinking towards math.” Participants also reported that content-focused professional development provided the content-specific learning needed for teachers to more effectively teach CMP3 curriculum. For example, one teacher stated,

And for me it’s like an eye-opener because I went through all that math and I never saw the connections but when I come and talk to you and do some Math Circles it’s like “Oh okay, that’s why I do that,” because sometimes I don’t know why I’m doing it I just know I need to do it, and this is how you do it. So, I like that part of [the content-focused activities]. (8th grade teacher, did not attend school-year PD).

A few teachers that did and did not attend the school-year PD were critical of the learning opportunities, communicating that the content was above their grade level and/or beyond their comprehension. When asked about the least effective aspect of the content-focused professional development, one participant within the focus group described not having to learn as much mathematics when she attended college many years ago. She explained that when the math was over her head, she got bored and did something else. She also stated that this did not make her any less of a math teacher. Another participant also communicated that the content was the least effective aspect of the professional development, and that it was wrong for the facilitators to assume the teachers had a strong mathematics background.

Application to teaching

Participants had mixed perceptions regarding if and how content-focused professional development may impact their teaching. Those participants who identified the training as effective felt they benefited from opportunities to increase their content knowledge, view mathematics from multiple perspectives, and implement many of the same activities from the training with their own students. Participants consistently communicated that increasing their own knowledge would positively impact their teaching and, thus, their students’ understanding of mathematics. One teacher stated, “If I learn something new myself I can take that and turn it around, and that will be beneficial, you know if my mind grows, that can be beneficial to my classroom” (6th grade teacher, did not attend school-year PD).

Many of the participants communicated that learning to examine problems from multiple perspectives would also have an impact on their teaching, as evidenced in the following quote.

I think too, the more we kind of stretch our brains, that gets delivered right back to the kids because now I have other ways to present content to them or show them multiple ways to solve problems that maybe I wouldn’t have even thought about had it not been for being exposed to Math Circles. (8th grade teacher, did attend school-year PD)

In a similar manner, other participants were more specific to how viewing problems from multiple perspectives would allow them to better serve struggling students.

Teachers were also able to see how many of the problems presented in the content-focused professional development could be effectively presented to their own students. One teacher reported that she often implemented problems from the content-focused professional development the very next day to see how her students would respond to the material. Likewise, a few participants felt the presented problems supported many of the lessons within CMP3 and were prepared to present the problems in class “like this morning’s activity tied directly into an activity that we do in that CMP3 curriculum. I mean, I’ve even made a note and I’ve already scanned the stuff and sent it to myself to use it” (8th grade teacher, did attend school-year PD). The teachers suggested that to continue implementing materials into their classroom, it would be helpful to provide them with detailed solution strategies written out following the activity. Teachers reported that it was difficult to record various solution strategies and to fully engage with the discussion of the problem at the same time.

In contrast, some teachers, several from sixth grade, reported that the math activities were not something that could be implemented with middle grades students. For example, one teacher stated, “I did not personally benefit from the Math Circles. While the Math Circles were challenging, they did not relate to my content and did not help me become a stronger teacher” (7th grade teacher, attended school-year PD). A desire for the problems to be more closely embedded within the CMP3 materials was also discussed with the need for greater attention to how to teach the specific mathematics versus how to do the mathematics.

A few teachers felt the content-focused professional development would have been more beneficial if they were separated by grade level and, thus, provided more grade-specific problems. Consider the reflection of one teacher:

I would like to do [the content-focused activities] in breakout sessions, much like we do our CMP stuffs. Being in the large group—with sidebar conversations, complaining that “I’m sixth grade … I can’t do this,” people who think it’s funny to act and respond as students would–can get very aggravating. I find myself actively NOT listening … I think breaking into small groups would help this, and possibly eliminate the problem. Breaking into small groups would allow [the content-focused activities] to be tailored to grade levels too, as the professors wouldn’t have to diversify their instruction, so as to appeal a little to everyone. (7th grade teacher, attended school-year PD)

Community building

Teachers were consistent in identifying collaboration, through active learning experiences, as a benefit of the content-focused professional development. When asked what the most effective aspects of the content-focused professional development were, multiple participants discussed opportunities to work with other teachers, specifically the benefits of collaborating when solving mathematics problems. For example, consider how one teacher discussed the support from the collaboration across Math Circle meetings:

You just started building relationships with teachers from magnet schools, from city schools, from county schools just to determine how did you approach this with your kids How did this work? And it will kind of encourage you to do it in your classroom, and then you begin to share resources and ideas and share lessons, and it just makes it, makes it fun and it makes it easier. (7th grade teacher, attended school-year PD)

Other ways in which collaboration was identified included providing opportunities to learn from peers and to engage with teachers from schools structured differently than their own.

Teachers also discussed how the connections at the content-focused professional development extended beyond the training. Teachers described remaining in touch through e-mail or phone calls to both share resources and to discuss topics not specifically related to math. One participant discussed the importance of maintaining communication with the other participants because they had received similar training and would, in turn, have similar perspectives. As another example, one teacher stated that she was not a “social butterfly” and that the content-focused professional development forced her to engage with other math teachers; because of this, now when she attends district mathematics trainings or meetings, she has relationships with other mathematics teachers, and this makes collaboration easier.

Factors Considered When Attending or Not Fully Attending Professional Development

Teachers identified multiple factors that they considered when deciding to attend or not attend content-focused professional development during the school year. Factors included administrative support and various school responsibilities, such as standardized testing and time out of the classroom. Each of these factors are discussed below.

Administrative support or permission

Teachers received varying support from their administrators to attend the school-year PD. One participant reported that her administrator valued teachers being in the classroom as much as possible, and thus she was not always permitted to attend. Other teachers felt their administration did not see the value in content-focused professional development. One teacher said, “I just couldn’t convince my principal enough that it was sufficient to miss school for, so I pretty much missed all but one” (7th grade teacher, attended school-year PD). These teachers attributed administrators not seeing the benefit from the professional development due to their limited mathematics background. Moreover, the teachers did not feel their administrators understood the type of professional development they needed to implement effective mathematics instruction—or even what effective mathematics instruction looked like. For example, a teacher who was not permitted to attend the school-year PD reported being reprimanded for allowing students to work in groups and for the noise that resulted from the academic conversations—an evidenced-based teaching practice (National Council of Teachers of Mathematics, 2014).

Other teachers reported complete autonomy in determining when to attend professional development during the school year. For example, one teacher stated that administration supported her attendance based on the reputation of the university-sponsored professional development. Another teacher stated, “I have the support. If I went to him and said I want to go, he would let me go just because he trusts me that I would make the best decision” (6th grade teacher, did not attend school-year PD). Interestingly, this teacher chose not to attend the year-long professional development.

School responsibilities

Participants identified how various school responsibilities affected their ability to attend the school-year PD. Most commonly, teachers reported scheduling conflicts with mandated testing; the partnering school district required end-of-quarter tests (EQTs) throughout the academic year. In addition to the actual EQT, teachers also reported needing to prepare their students or to review in the weeks leading up to the EQT. Additional state-mandated standardized tests in the spring of each year were also mentioned as causing a conflict in attending the school-year PD.

Another factor the teachers discussed was time away from students when attending professional development. For example, one teacher was not convinced that the school-year PD was worth an entire day away from her students. Another teacher reported missing close to 18 school days within the last academic year due to various professional development workshops. Time away from students likewise required a substitute. Many teachers stated finding a substitute was difficult, or the time needed to plan for a substitute presented a challenge. Another participant stated that she teaches at a very small school and if more than one teacher is out on any given day, it feels as if there is a limited teacher presence at the school.

When asked if participants would be more willing to attend professional development offerings after school, the teachers were divided. Some expressed that after school offerings would alleviate time away from students, while others stated that commitments to extra-curricular activities, family, and personal life would not permit them to attend.

Discussion

Results from the current study revealed what middle grades teachers who participated in content-focused professional development perceived as effective and ineffective, as well as the factors that impacted their participation. How teachers perceived the content-focused professional development activities will be discussed in terms of Putnam and Borko (2000) situative perspective. A discussion of the factors impacting teachers’ attendance will follow and focus on administrative support and school responsibilities.

Effectiveness of Content-focused Professional Development

The first of Putnam and Borko (2000) central aspects is that learning is situated: that the context or environment within which learning opportunities are presented impacts what is learned. Furthermore, Putnam and Borko posited that the familiarity of a teacher’s own classroom can be a barrier to learning and growth and that summer workshops can offer a new context for learning which benefits teachers. The teachers participating in the current study identified opportunities to improve their own mathematical content understanding as an effective aspect of the training. This improvement was recognized by the participants as benefiting both their teaching and their students’ mathematical understanding. This suggests that the learning opportunities within the content-focused professional development were appropriately situated for most teachers (Putnam & Borko, 2000). Teachers’ also reported that examining mathematics problems from novel perspectives led to new learning, as well as opportunities to think and reason in ways similar to those required of their students in the CMP3 curriculum. Hill, Ball, and Schilling (2008) found that teachers with strong mathematics content knowledge often provide richer and more consistently rigorous mathematics instruction to students, which supports students’ mathematical understanding. An increased understanding of the mathematics content has also been shown to equip teachers with the knowledge, skills, and dispositions needed to implement best practices in the mathematics classroom (Ball et al., 2005; National Council of Teachers of Mathematics, 2014; Swackhamer et al., 2009).

The second of Putnam and Borko (2000) central aspects is that learning is social: that learning is impacted by interactions with others, and teachers can learn from one another when collaborating within a learning community. The teachers participating in the current study were able to develop a community within the context of the training, specifically with teachers from different schools and that taught different grades. This is in contrast to previous research recommending that professional development is most effective when there is collective participation from teachers at the same school or department (Desimone, 2009; Garet et al., 2001). Perhaps the value of new voices and perspectives experienced by participants in the current study outweighed the benefits of collective participation described in the literature (e.g., Garet et al., 2001; Main & Pendergast, 2015).

Beyond developing community, participating teachers often described the benefits of learning alongside other mathematics educators. When solving challenging mathematics problems, teachers reported immense value in seeing others’ reasoning and perspectives as they solved the problem. Wei et al. (2009) found that giving teachers opportunities to view and anticipate how others would reason about and respond to mathematical tasks can benefit teachers’ instruction and their ability to facilitate mathematics discussions in their own classrooms. The effectiveness of collaborative experiences within the content-based professional development may have contributed to the teachers’ positive learning outcomes as well as to the success teachers reported in implementing content-focused activities in their own classrooms.

The last of Putnam and Borko (2000) central aspects is that learning is distributed: that knowledge is “stretched over,” or distributed among other individuals and/or artifacts. In alignment with Hodgen (2011), it would be expected that the teachers within this study situated their mathematics knowledge—to varying degrees—within their curriculum resources and the immediate context of their classroom. It would also be expected that those with elementary grades certification were more often less secure in their mathematics knowledge than those with secondary grades certification (Hodgen, 2011). Cognition, as distributed, provides one explanation for why the teachers in the current study varied in their abilities to view connections between opportunities to increase their own content knowledge and their teaching. Given that the content-based training activities often engaged teachers with mathematics problems in a novel setting, thus situated outside of the curriculum and classroom setting, teachers with elementary grades certification may have viewed these learning opportunities as less effective. This might explain much of the critique regarding the content-focused activities, especially from sixth-grade teachers. If a teacher’s knowledge is heavily situated within the context of his or her classroom and specific grade-level curriculum, any opportunities to reason with mathematics beyond such materials may be received poorly.

Factors Impacting Attendance

Although literature about effective professional development recommends that training includes a substantial number of contact hours and be sustained over time (Clarke & Hollingsworth, 2002; Desimone, 2009), identifying common days and times for teachers to attend proved challenging. Factors participants described related to deciding to attend or not attend the school-year PD were school-level characteristics, including various school responsibilities and lack of administrative support (Krille, 2020; Phillips et al., 2011; Wan & Lam, 2010). Of these, scheduling conflicts with mandated testing—resulting in lack of time to attend—was the most commonly identified obstacle to teachers attending the training. This finding was similar to Wan and Lam (2010), with lack of time being the most common identified factor hindering teachers from attending continued professional development. Aside from scheduling conflicts and time constraints, teachers discussed difficulties with scheduling and planning for substitute teachers, as well as time away from students, as deterrents for attending professional development offerings. Similarly, Wan and Lam (2010) suggested that teachers were more likely to attend professional development workshops if administrators and colleagues were more helpful in finding substitutes for the teachers attending the workshops.

Participants also reported that administrators held varying views of content-focused professional development. Participants who had more autonomy and administrator support were more likely to attend the professional development throughout the school year. Phillips et al. (2011) also found that teachers with principals who were invested in their professional growth were more likely to attend trainings outside of school. The participants also reported that administrators’ misguided perceptions of effective mathematics instruction were one reason for not receiving support to attend the training. However, even when teachers had full support from their administrators to attend, some teachers decided to not attend. More personal factors such as time with family and extra-curricular activities were also factors in teachers considering whether to attend the content-based professional development (Krille, 2020; Maloney & Konza, 2011).

Conclusion

The purpose of this study was to determine how middle grades mathematics teachers perceive content-focused professional development. More specifically, the study examined the perceptions of the teachers regarding the effectiveness of the training and the factors teachers considered when deciding to participate or not fully participate in the training. To address each of these questions, focus group interviews and surveys from middle grades mathematics teachers were collected and analyzed. The design of this study provided a unique research opportunity as data were also collected from those teachers who were invited but did not attend the school-year PD. This research opportunity is not often available when examining why teachers do or do not participate in professional development because data are typically collected only from those who attend.

This study suggests that content-focused professional development allowed middle grades mathematics teachers an opportunity to deepen their mathematical content knowledge. Participants also identified multiple effective aspects of the training, including application of new learning to their classroom instruction and engagement in a community of mathematics educators. Even so, the attendance during the school-year PD remained highly variable. In addition to the obstacles that teachers identified in attending the professional development—school responsibilities and lack of administrative support—how teachers perceived the training may have also impacted their commitment. When attempting to removing barriers similar to those identified in this study, equal importance should be given to creating professional development opportunities that meet the needs of each and every participating teacher. Regardless of whether teachers are supported in attending content-focused professional development, unless they view this training as worthwhile, they will likely not attend (Maloney & Konza, 2011).

Limitations

While the study provided potentially useful findings regarding content-focused professional development, a number of limitations have been identified. First, the sample size was limited to 23 teachers, with fewer than 10 in each of the three participating grade levels. Prior to making any generalizations regarding the professional development needs of teachers from a specific grade level, a similar study with a larger sample size should be conducted. Second, the teachers within the study were primarily from high-needs schools. We recommend future studies consider middle-level teachers’ perceptions from a range of school settings.

Implications

The results of this study can inform administrators, mathematics teacher educators, and professional development providers. First, for teachers to successfully implement a reform-oriented curriculum, such as CMP3, conversations and/or training with middle school administrators are needed. Given all participating teachers were from low-performing schools, it is possible that administrators valued teachers being present for instruction versus attending professional development. However, given the demands of the reform-oriented curriculum, teachers reported a need to increase their own mathematics content knowledge. Because not all administrators have a mathematics background, conversations, and training with administrators regarding effective mathematics instruction and the knowledge needed to teach mathematics effectively are needed. Likewise, because those teachers who need to increase their content-specific knowledge are the least likely to attend such training, administrators are key to ensuring students are provided with knowledgeable and effective mathematics teachers (Desimone et al., 2006).

Second, professional development that spans multiple years requires continual efforts to maintain administrative and district support. Although the project was initially supported by both the district and school administrators, over the years the leadership changed and many of the participating teachers reported decreased support. Similarly, Jacob et al. (2017) noted that, over time, changes in administration impacted the once received support and teacher attendance waned later in the project.

Third, teachers should be provided with opportunities to examine where and how their mathematics knowledge for teaching is situated. One possible activity could include having teachers create a math autobiography to examine their learning experiences related to mathematics. Darling-Hammond and Hammerness (2005) identified empirically grounded teacher learning practices, one of which included awareness and consideration of personal education and autobiography.

Lastly, the design of professional development should take into consideration the grade-band—primary versus secondary—of the attending teachers and how those teachers might situate their mathematics knowledge for teaching. For example, if primary grades teachers are attending, opportunities to increase subject matter knowledge must be closely connected with the context of the classroom (Hodgen, 2011). These opportunities may include designating a portion of the professional development to grade-level sessions. A second suggestion includes using the adopted school curriculum as one resource on which to focus the content-specific professional development.

As the content-focused training continues beyond the data collection included within this study, it is our hope to share how each of these implications, and recommendations for future research further informs and/or shifts middle grades mathematics teachers’ perceptions of content-focused professional development.

Additional information

Funding

This research was supported in part by a grant from the Alabama State Department of Education under Grant [U700180]. Prime Sponsor: US Department of Education (ED).

Appendix A:

End-of-Experience Survey

1. How much did you participate in the Math Circles and other MSP professional development during the school year?

   1. Attended all activities

   2. Attended most activities

   3. Attended less than half of the activities

   4. Did not participate during the school year

2. How much did you participate in the summer workshop?

   1. Attended all sessions

   2. Attended 75% or more of the sessions (missed 1 or 2 days)

   3. Attended 50–74% of the time (missed 3–4 days)

   4. Attended less than half of the sessions (missed 5 or more days)

3. What grade level do you teach (if you work with more than one, indicate which grade level you worked with during the workshop)?

   1. 6^th

   2. 7^th

   3. 8^th

4. What was the most effective aspect of your experience with the Math Circles during the workshop?

5. What was the least effective aspect of your experience with Math Circles during the workshop?

6. Please indicate what grade level you teach (check all that apply)?

   1. 6^th

   2. 7^th

   3. 8^th

7. What type of certification do you possess (check all that apply)?

   1. Elementary

   2. Special Education

   3. Secondary Mathematics Education

   4. Middle School Mathematics Education

   5. Other (please specify):

8. How many years have you taught middle school mathematics?

   1. 0–2 years

   2. 3–5 years

   3. 6–9 years

   4. 10 or more years

Appendix B:

Focus Group Interview Questions

1. How would you describe what takes place in the Math Circles?

2. What do you consider when determining if you can or cannot attend a Math Circle meeting?

   1. What challenges do you face in attending Math Circles (prolonged professional development)?

   2. If you do attend, what affects that decision to attend?

3. What is the most effective aspect of Math Circles?

4. What is the least successful aspect of Math Circles?

5. How important is increasing your mathematics content knowledge? Are there other areas of teaching that you feel are more important to develop?

6. Do you feel you have your administrator’s support to attend Math Circles?

7. Do you feel you need a support community (professional learning community) beyond your current school setting?

8. How likely are you to communicate with those who attend Math Circles outside of Math Circle meetings?