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From Cloud to Classroom: Mathematics Teachersí Planning and Enactment of Resources Accessed within Virtual Spaces


by Sihua Hu, Kaitlin T. Torphy, Kim Evert & John L. Lane - 2020

Background/Context: Teachers face many different problems in teaching. Traditionally, research examines the complexity of teaching students and content by focusing on a teacherís physical space and influencing factors therein. While established conceptions of curricular enactment suggest that instructional materials shape both the intended and enacted curriculum, the materials themselves are traditionally conceived of as those that the district officially adopts (e.g., textbooks) or creates (e.g., curricular pacing guides). Yet, in 21st-century schools, a new era of information and technology presides. Facilitated by the cloud, teachersí professional learning and interactions meld with a global network of colleagues, extending to community of practices online and curating instructional resources therein. In particular, the use of social media to broaden and deepen teachersí access to instructional resources is a potentially transformative and yet disruptive phenomenon that has implications for classroom instruction. Narrowly focusing on districtsí official curriculum and its enactment by the teacher as an individual who is shaped by (but does not shape) her school landscape may not, in fact, fully reflect teacher professionalism today and account for teachersí professional life in the social continuum from cloud to class.

Purpose/Objective/Research Question/Focus of Study: Situated in the conceptualization of managing problems in teaching and curating online resources as informal learning for the intended and enacted curriculum, this article builds on and extends these lines of research to examine teachersí leverage of social capitalósocial network among individuals and resources available to people within their social networkófrom the virtual space to solve the problems common to teaching. Through this empirical illustration of resource diffusion from cloud to class, and how the curation of resource is integrated with teachersí curriculum planning as well as classroom practices, we present a unique way of understanding teachersí management of teaching problems in 21st-century schooling.

Research Design: We collected various types of data from 67 early-career teachers in one Midwestern state, including interviews, observation, and survey. We drew primarily on the interview data to exemplify our conceptual model of curation to address the problems of teaching. The three curation processes we identified are: (1) self-directed curation, (2) incidental curation, and (3) socialized curation. We observed more empirical evidence on the self-directed curation process in our data and chose to select a single case to go into further detail about the enactment of online resource in the classroom using the observation data, in additional to the interview data. We analyzed the case by specifying the perceived problems of teaching in one teacherís preparation to teach and how the curated resources from Teachers Pay Teachers were adopted and adapted to manage each of the problems, and the teacherís rationale for the decisions she made during the planning. We noticed, in this case and in other data that we have across teachers, that teachers rarely, if ever, directly articulate the curation of online resource for preserving classroom order, among the four endemic problems identified in the literature. Last, we examined the enactment of the online resource by describing teachersí instructional practices in relation to her perceived ways of managing the problems of teaching. We also examined the resulting student learning in the mathematics lesson we analyzed. The single case of one teacher serves as an empirical illustration of how teachers could curate resources from the cloud in their planning and enactment of curriculum.

Conclusions/Recommendations: At the core of this study, we see teachers taking up their agency and drawing on a particular type of social capital resource to manage their enduring problems of teaching. We identified the different paths that teachersí social capital may travel and accrue, and we argue for the importance of the community of practice online in the facilitation of resource flow from the cloud to the classroom. Also, we used a mathematics teacherís planning and enactment of instructional resources attained from the cloud for a three-day lesson series as an example to demonstrate how perceptions of teaching problems and curations of materials can culminate in a teacherís actual practices and impact student learning in the classroom. Our work has several implications for the field. First, although the different problems in teaching are well documented, teachers tend to seek out social capital resources from the virtual spaces to address some, but not all, of their problems. Specifically, preserving classroom order has not been present in our analysis of teachersí articulation of their perceived problems for curation. Future studies can add more understanding to the online resources used in relation to teachersí modes of curation and the type of teaching problems they hope to address. Second, the process of accessing the instructional resources, as delineated in the three modes of curation, demonstrates the complexity of the social network and social capital accrual mechanism in the 21st century, through which teachersí professional communities expand beyond the school walls. Third, our work presents the considerations and thought processes of teachersí curation of instructional materials in virtual spaces and enactment of the tasks. The combination of social capital resources and classroom processes in this study provides the foundation for researchers with different perspectives to further investigate the emerging phenomenon of social media and education.

Teachers face many different problems in teaching. Problems arise not only from the intellectual domain of teaching and learning but also from the social and temporal domains (Lampert, 2001). The complexity of teaching occurs as one must navigate through various problems, often simultaneously. To solve these problems, teachers have to consider the context and domain in which the problems arise in order to take action.


Teaching is more than managing the relationship with students and content in the classroom. Teachers, as beings in social contexts, are constantly interacting with the larger community they are situated within, such as administration, other teachers, students, and family. As Lampert (2001) put it, “What a teacher is doing in any instance of teaching with a particular student and a particular content is part of an ongoing stream of action and interaction set in a wider curriculum and a larger social environment” (p. 35). Working with different groups of students in various social structures across time and content adds another layer to the complexity in teaching.


Traditionally, research examines the complexity of teaching students and content by focusing on a teacher’s physical space and influencing factors therein. These studies tend to look at how teachers exercise their agency to negotiate boundaries in their profession and how they interact with students and content in the classroom within an organizational context (e.g., Ball & Forzani, 2009; Coburn, 2001; Spillane & Jennings, 1997). Although established conceptions of curricular enactment suggest that instructional materials shape both the intended and enacted curriculum, the materials themselves are traditionally conceived of as those that the district officially adopts (e.g., textbooks) or creates (e.g., curricular pacing guides) (Remillard & Heck, 2014). Yet, in 21st-century schools, a new era of information and technology presides. Facilitated by the cloud—a virtual ecosystem enabled by servers with unique functions around the globe (Microsoft Azure, n.d.)—teachers’ professional learning and interactions meld with a global network of colleagues, extending to community of practice online and curating curriculum materials therein (Bieda et al., 2017, 2020; Hu et al., 2018; Torphy et al., 2017). In particular, the use of social media to broaden and deepen teachers’ access to instructional resources is a potentially transformative and yet disruptive phenomenon that has implications for classroom instruction (Torphy et al., 2017). Narrowly focusing on districts’ official curriculum and its enactment by the teacher as an individual who is shaped by (but does not shape) her school landscape may not in fact fully reflect teacher professionalism today and account for teachers’ professional life in the social continuum from cloud to class.


Situated in the conceptualization of managing problems in teaching and curating online resources for the intended and enacted curriculum, this article builds on and extends these lines of research to examine teachers’ leverage of social capital—social networking among individuals and resources available to people within their social network (Bourdieu, 1986; Coleman, 1988)—from the virtual space to solve the problems common to teaching.  In this article, we scrutinize a sample of early career teachers’ (ECTs’) ways of accessing instructional resources from a salient virtual resource pool (VRP) and provide an example for how resources from the cloud shape curriculum planning and enactment in the classroom. Through this empirical illustration of resource diffusion from cloud to class and of how the curation of resources is integrated with teachers’ curriculum planning and classroom practices, we present a unique way of understanding teachers’ management of teaching problems in 21st-century schooling.


BACKGROUND AND CONCEPTUAL FRAMEWORK


UNDERSTANDING THE PROBLEMS OF TEACHING


To examine the challenges that teachers encounter, we use Kennedy’s (2016) taxonomy for parsing shared professional problems. The taxonomy centers on four enduring dilemmas of teaching: portraying content, enlisting student participation, eliciting student thinking, and preserving classroom order.


Portraying Content


The core act of teaching is bringing students into meaningful interaction with academic content (Cohen et al., 1993; Elmore et al., 1996; Lampert, 2001). Namely, teachers must attend to how they will portray the curriculum to their students and to how they envision students will engage with the content once presented (Kennedy, 2006). In other words, teachers must translate the official curriculum (constructed from content standards, district-endorsed instructional materials, district pacing guides, assessments, and the like) into an intended curriculum that they will ultimately enact in their classrooms while also balancing the demands of the official curriculum, their own interpretations and pedagogical commitments, and the teachers’ perceptions of students’ skills, abilities, and interests (Remillard & Heck, 2014).


Teachers, then, use instructional materials and other resources to devise a plan for activities that will bring students in close contact with important academic content; they then attempt to realize these plans in real time with students in classrooms (Kennedy, 2016; Lampert, 2001). As a recurring challenge of teaching, portraying content in productive ways thus requires expertise and judgment as teachers build their capacity in both planning and enactment over time (Borko & Livingston, 1989; Kennedy, 2016).


Enlisting Student Participation


Because learning is difficult, students must embrace the goal of mastering new material if they are to excel academically (Cohen, 2011; Lampert, 2001). However, rather than taking participation for granted, teachers must work to secure student commitment (Jackson, 1968; Kennedy, 2005). Thus, enlisting student participation is the second of the chronic challenges of teaching in Kennedy’s (2016) taxonomy. Several conditions endemic to teaching make securing student commitment difficult. As Cohen (2011) noted, the “social resources” available in other occupations are notoriously weak in teaching.


First, the content of what is to be learned is often disputed both within the classroom and beyond. For instance, teachers might regard subjects that are of great interest to students as having very little academic value. Likewise, students may find little value in achieving competency in academic subject matter that has little bearing on their everyday lives (Cusick, 1973, 1992; Wolcott, 1974). Second, the means of education are also disputed. The United States has long been divided about the nature of knowledge and about how students learn best (Cremin, 1990; Cuban, 1993; Ravitch, 1983). Finally, the outcomes of schooling are contested; there are long-standing disagreements about whether schools are supposed to promote universally high levels of learning for all students, distinguish students along a continuum that spans from achievement to nonachievement, or prepare students for the needs of the economy (Labaree, 1997; Parsons, 1959).


Because the curriculum objectives, pedagogical approaches, and ultimate outcomes of schooling are constantly debated and because schools face pressures to demonstrate acceptable levels of achievement and attainment of all students, teachers find it difficult to consistently secure students’ academic commitment (e.g., Cusick, 1983; Labaree, 2010). One, albeit unsavory, solution to this dilemma is to allow students to select classes with levels of academic rigor to their liking while the teachers and students work out “bargains” in which teachers relax their academic expectations in exchange for student attendance and good behavior (Cusick, 1983; Powell et al., 1985; Sedlak et al., 1986; Sizer, 1985).


Eliciting Student Thinking About Content


Eliciting student thinking about content is a third major challenge of teaching in Kennedy’s (2016) framework. When eliciting student thinking, teachers attempt to determine what the students think about the content and how far the students’ understanding has advanced. Eliciting student thinking is a difficult endeavor for several reasons. First, and related to the point mentioned earlier, student commitment to academic matters—and, by extension, their obligation to disclose their thinking about content—is often tenuous. Second, students are novice thinkers, and their understanding (or misunderstanding) of content can be confusing for teachers to deal with and make accommodations for in the moment (Borko & Livingston, 1989; Kennedy, 2005; Lampert, 2001). Additionally, teachers may have more trouble extracting and understanding student understanding because of the considerable social distance between teachers and their students (Jackson, 1968) and because the students themselves are often unprepared to talk about their learning in ways that others can easily understand (Kennedy, 2005; Lampert, 2001). Finally, teachers may also choose not to elicit or further elicit student thinking during certain moments of teaching because they are concerned about making the student uncomfortable in front of peers. Attending to student thinking, understanding what to share, and deciding how to respond demonstrate the complexity of teaching and the difficulty to elicit student thinking; these practices often, as Jacobs et al. (2010) put it, “happen in the background, often simultaneously, as if constituting a single, integrated teaching move” (p. 173).


Preserving Classroom Order


Representing content, securing student participation, and accessing student thinking all occur in a context in which teachers must preserve classroom order and ensure that students are behaving themselves appropriately. Because teachers must orient students toward academic matters and access their thinking about academic content even when the students would rather they did not, managing student conduct is a persistent challenge (Becker, 1953; Jackson, 1968). This challenge has intensified in recent decades; expectations for student academic achievement have increased while teachers’ ability to control student behavior through corporal punishment or other draconian means has diminished (Cusick, 1992). Thus, teachers must think carefully about how they will get students to behave and commit to classroom activities.


The challenge of preserving classroom order is further complicated by forces outside the classroom. Namely, parents have great interest in how they perceive their children are being treated in schools, and this concern limits how teachers can secure classroom order. Furthermore, parents in different social and economic circumstances engage with schools and support (and challenge) teachers’ work differently. For instance, middle- and upper-class families amplify the academic programs of the school and support the moral order of the school that acknowledges the rightful authority (within limits) of the teacher (Becker, 1953; Lareau, 1987). Yet, these same parents feel free to question the teachers’ professional competence in matters salient to their children’s academic experiences and may expect that their children be treated as miniature adults (Becker, 1953; Lareau, 1987; Metz, 1978a). Middle- and upper-class parents are also likely to encourage their children to contest the intellectual and moral authority of the teacher when their interests are threatened (Metz, 1978a). In contrast, although lower class parents are less likely to contest the teacher on academic grounds and less likely to press for their children’s academic advantage, they are sensitive to what they perceive to be unfair treatment of their children and may be less likely to recognize the school’s and teacher’s moral authority (Metz, 1978a, 1978b).


Finally, not all teachers’ difficulties stem from student defiance or intentional misconduct. Classrooms may be difficult to manage even when students are committed to learning. Teachers may want students to engage in content, but unexpected interruptions, such as a phone call in the middle of a lesson, or pulling out of students for special instruction, can challenge the order of the classroom (Kennedy, 2005). On the other hand, too much attention to classroom order can stifle creativity and inhibit learning (McNeil, 1985). Thus, teachers are likely to try to find a balance, which may differ by the composition of the class (Metz, 1978a, 1978b).


RESOURCES FOR TEACHERS TO MANAGE PROBLEMS IN TEACHING


When dealing with challenges of teaching, teachers are not left entirely to their own devices. Rather, teachers have social and physical resources to draw on (Lampert, 2001). Specifically, although some scholars have argued that the infrastructure of resources for teaching is weak (e.g., Cohen, 2011), most teachers have material resources they can use (e.g., curricular frameworks, standards, and instructional materials) to construct an intended curriculum that will help them portray content to students and elicit student thinking. Teachers also have social resources in the classroom that develop as they construct relationships with students over time; these relationships help establish a positive environment for learning and expectations for how students are to interact with content and with each other (Lampert, 2001). Finally, teachers have access to social capital resources from communities of practice to help them implement curricular initiatives and learn about reform practices (e.g., Coburn et al., 2013; Frank et al., 2004; Sun et al., 2013). Within these networks of colleagues connected by interpersonal relationships, teachers may receive additional information, advice, and support from their peers and generate new professional knowledge within the community (Bidwell & Yasumoto, 1999; Coburn et al., 2012).  


As an emergent phenomenon, the kinds of resources teachers turn to in their networks within and outside their school manifest themselves as curricular materials. In a national survey conducted by RAND (Opfer et al., 2016), almost all teachers reported using Google for professional purposes. In addition, more than 87% of elementary teachers and 51% of secondary teachers reported the use of the social media outlet Pinterest and the online marketplace Teachers Pay Teachers (TpT) for acquisition of instructional materials aligned to the national curricular policy, Common Core State Standards (CCSS). In our surveyed sample of ECTs from three Midwestern states, we found results similar to the RAND report with regard to teachers’ use of Pinterest and TpT. About 80% of the teachers reported these VRPs as the top two social capital resources they turned to for mathematic instructional materials for teaching at least once a month, and about half of them reported using one or both at least once a week (Hu et al., 2018). This suggests that teachers leverage social capital resources from a global network of colleagues who may face problems in the classroom that are similar to theirs. In response to perceived problems of the local curriculum, teachers may seek out additional information and resources within their physical and virtual social networks and within and beyond the school walls.


CONCEPTUAL FRAMEWORK TO MANAGE TEACHING PROBLEMS WITH SOCIAL CAPITAL RESOURCES


In this study, we do not view teachers as passive implementers of curriculum but instead as active problem solvers of local dilemmas that in return shape how curriculum is conceptualized and enacted in their classrooms. Accordingly, they may consult many sources and take various learning paths to find ways to address problems in teaching. Among these resources, social capital resources available in the virtual spaces are one of the main venues for them to leverage collective wisdom from a larger network of colleagues and knowledge of practices in the global professional community. Researchers have discussed social capital resources leveraged by teachers in two interconnected forms. One well-studied social capital resource from the cloud is the advice and help that teachers receive from a network of colleagues, and the sense of belonging to the community (Carpenter & Krutka, 2014; Kelly & Antonio, 2016; Ranieri et al., 2012; Rehm & Notten, 2016). Emergent from recent research is another form of social capital resources—the instructional materials that teachers individually and collectively generate and diffuse among those trusted others (Hu et al., 2018; Opfer et al., 2016). While the former body of studies focuses on the structural relationships among teachers in the community of practice online, studies in the latter category add value to the field by investigating the particular resources and content of those resources as embedded in these social relationships. Both of these types of social capital resources that teachers may access constitute the knowledge and practices in their learning environment to address problems they encounter in their classrooms.

 

We situate the access and sharing of instructional materials as social capital accrual and diffusion in the notion of curation. Based on Bhaskar (2016), curation is about synthesizing information and locating useful ideas and materials to form meaningful collections. These collections can provide new perspectives for the curators themselves as well as for those who see (or consume) them. By curating within virtual spaces and leveraging social capital in the process, teachers share their collections of resources and ideas with one another in a community of practice online, and they work individually and collectively to find a way to solve the problems in teaching.


We draw on Schugurensky’s (2000) conceptualization of informal learning to theorize teachers’ modes of curation within social media. Using two indicators—intentionality and consciousness—Schugurensky identified three forms of informal learning: (1) self-directed learning; (2) incidental learning; and (3) socialization. According to the author, self-directed learning is both intentional and conscious at the time of learning, exemplified by a teacher who faces a particular teaching problem and seeks out solutions purposefully. Incidental learning, in contrast, is unintentional, but the individual is aware as learning occurs. For example, a teacher may run into a strategy to manage one of his or her perceived problems in the classroom when browsing websites in his or her spare time. The third form of learning—socialization—is neither intentional nor conscious. Schugurensky regards this form of informal learning as the internalization of values, skills, aptitudes, and behaviors in the process of participating in the community and adopting norms. This conceptualization is similar to the situative perspective of learning, as teachers develop knowledge for teaching when they enculturate to norms and practices within the community of practice as participants (Lave & Wenger, 1990; Wenger, 1998). This theory, however, is not specific to teacher learning. Moreover, it does not consider the space where the learning occurs. By taking this framework of informal learning and reapplying it in the new context of social media, we capture teachers’ leverage of social capital resources through introducing the notion of curation in place of “learning.” Additionally, we incorporate the perceived problems of teaching in the curation processes to understand teachers’ professionalism in these practices.


Ultimate solutions to the enduring challenges of teaching may be unavailable, for they constitute a set of competing dilemmas that therefore must be managed rather than solved (Kennedy, 2005). In this article, we examine how teachers tap into a particular type of resource—instructional materials in virtual spaces—to help them manage the endemic challenges of teaching. Although other works have identified virtual resources accessed online as a particular social capital resource that teachers often turn to, there is a lack of understanding about the implementation of those materials and how they affect classroom and student learning. It is important for the field to understand what kind of virtual resources teachers procure and how those resources are integrated into instruction and learning within the classroom. The social capital resources from cloud to classroom may have serious implications for teacher educators and policy makers to promote teachers’ agency and further support instruction by capitalizing on existing practices of teachers.


The virtual spaces that teachers engage in frame how teachers engage—that is, for acquiring and sharing resources or engaging in educational discussions—and the resources accessed frame what teachers plan and enact in the classroom. In this article, we seek to examine the different ways that teachers may curate the instructional resources from the virtual spaces to manage their perceived problems of teaching, and we provide empirical illustration on how such an acquired resource can be enacted in the classroom.


METHOD


This study is situated within a larger study on K–5 ECTs’ practices as shaped by the social norms in their schools and by the career and college readiness movement, such as the enactment of CCSS. ECTs were defined as teachers in their first four years of teaching at the time of the study. To enroll participants, we first attained agreement from the district leaders and then sent invitations to all eligible ECTs in the district to participate. The larger study collected various types of data over the course of three years. The types of data collected included surveys, classroom observations, and interviews. In this study, we focused on data collected in the second year, and we included participating ECTs in one Midwestern state as our sample. These ECTs were chosen because they contribute to the largest proportion of participants in the larger study, and we were able to collect video of teachers’ mathematics lessons for observation data. This particular state withdrew from the CCSS and transitioned to a set of similar state standards for their overarching curriculum right when the project started. Despite the common policy context to follow the state standards of mathematics, the four districts examined in this state mandated different teacher instructional expectations, and they differed in their curricular policy and implementation in terms of textbook selection and adaptation, pacing requirement, and fidelity to the official curriculum. The diversity in contexts allowed for more variance in the types of teaching problems that teachers encountered and how they leveraged social capital resources from the virtual spaces.


DATA SOURCES AND ANALYSIS


Semistructured Interviews


We conducted two 20-minute interviews during the school year, one in the fall and one in the spring. The interviews were conducted by researchers within one day of observing teachers’ mathematics instruction in the classroom. In these semistructured interviews, we asked participating teachers to reflect on their planning of the lesson observed to get a sense of their thought processes in their preparation to teach. Because we sought to answer the question of how teachers plan with the instructional resources they curated in virtual spaces and enact them in their classrooms, the interview questions we asked included what resources they use, how they decide on the content, and the ways in which they collaborate with colleagues. In answering these interview questions, teachers often discussed their general lesson planning practices as they reflected on the similarities and differences of their planning for “today’s lesson.” The questions in the interview allowed teachers to tell us about their school and district context and identify the sources of instructional materials before prompting for the rationale behind the choice. Interviews were audio-recorded and then transcribed by the research team members. Through the lens of the four types of teaching problems delineated in the literature, we coded the interviews and identified the specific teaching problems that each teacher perceived in their practices and how these teachers linked these problems to their consultation of the cloud and modes of curation.


Survey


We collected survey data from all ECTs (n = 99 in the second year) within the larger project twice a year. In the survey, we asked teachers how often they consulted different social media and VRPs online for their mathematics instruction, and the purposes for which they used each platform. We used the survey data to compare what teachers routinely do with the interview data and confirmed our hypothesis that there was a salient phenomenon of using social media and some other VRPs in sampled teachers’ (n = 67) teaching practices, despite the diverse contexts of the districts and schools. Even in one of the sampled districts from our focal state, where there was a strict requirement for fidelity to a prescribed official curriculum, we observed teachers supplementing the textbook by using virtual resources in one way or another, finding the room to address the teaching problems with additional resources. The survey data also provide support for our use of interviews and observations for insight into a teacher’s practices even though they were only a snapshot of what happened over a school year.


Uses of Observations


As mentioned earlier, we collected video recordings of teachers’ mathematics instruction for the larger study. We used the interview coding to guide us in selecting the observations with elements of using instructional resources from the cloud. From coding of 134 interviews collected from 67 teachers in the Midwestern state of focus, we found 141 instances of the use of some online resources, among which 49 were specifically used in the lesson we observed before the interview. Eventually, we decided to zoom in on one case of a teacher and her enactment of online resources (Yin, 1984), and we used the coded interview with this teacher to help us interpret her practices. The reasons are manifold. First, this teacher shared several commonly perceived teaching problems identified within our larger sample (e.g., how to keep students engaged, what skills need to be reinforced with the content delivery). Additionally, she used the instructional resources accessed online for the core part of the lesson, rather than just for certain activity structures within the lesson (e.g., center time or daily routine time). Furthermore, although we planned to select multiple cases to illustrate the enactment of instructional resources acquired from each mode of curation, we were not able to find any observation videos that included the use of particular virtual resources acquired from incidental curation and socialized curation for the core part of the lesson. Enactment of instructional resources acquired through these two processes in the cloud tend to be used in certain activity structures, such as center time and warm-up activity. Most of these activities were largely student initiated and did not involve a significant amount of interaction between the teacher and the students. As a result, we chose to focus on finding one case of enactment associated with self-directed curation, which is the most salient behavior in our data. Last but not the least, what is more interesting in this teacher’s case is that she not only enacted the instructional resources accessed from virtual spaces the day we interviewed her, but she actually talked about a three-day lesson sequence in her interview and how she planned lessons that connected with one another across observations. We as researchers were there in her classroom for the second and third day of the lesson sequence to capture the use of the mathematical tasks taken from TpT over this lesson trajectory.


By transcribing the video verbatim, we analyzed this teacher’s moves as she interacted with students around the instructional task, how that corresponded to the different problems perceived by the teacher, and ways that she tried to manage the teaching problem in action. By identifying the bridges (and the lack thereof) between the teacher’s intention in planning (intended curriculum) and her actual enactment of a virtual resource in teaching (enacted curriculum), we provided a comprehensive picture of a teacher’s use of social capital resources as a way to address curricular insufficiency and to meet her students’ needs.


THE CURATION PROCESSES IN PREPARATION TO TEACH MATHEMATICS


In this section, we present coded excerpts from the sampled 67 teachers’ interviews to exemplify our conceptual model of teachers’ curation for the purpose of managing problems of teaching. In discussing their preparation to teach the mathematics lesson, teachers’ descriptions of the curation of resources from the cloud largely followed the modes observed in the informal learning literature. We argue, however, that the cloud has become a new space where teacher learning can happen, and the teaching problems that teachers perceive play an important role in these different processes. Specifically, we found that in our data, managing the problem of teaching can be the primary driving force and/or the end goal of the curation processes. Specifically, the three modes of leveraging social capital resources from the cloud are (1) self-directed curation, (2) incidental curation, and (3) socialized curation. In Figure 1, we provide a visual representation of the processes.


Figure 1. Conceptual model of the problem management processes


[39_23307.htm_g/00002.jpg]


Note: The picture in the figure represents Pinterest, an example of a virtual resource pool where teachers

access instructional resources predominantly.


SELF-DIRECTED CURATION


When teachers perceive a problem in their teaching, they often purposefully seek out ways to address their problem, and social media may be one of the places to which they turn. This particular process is intentional—a teacher has a clear delineation of the perceived problems in his or her teaching and takes the initiative to find what is needed to manage the problems. Within our sampled teachers, many of them talked about their access of instructional resources online being self-directed. One fourth-grade teacher said,


So we kind of, well since it’s close to Christmas to keep them engaged we try and theme things. So today everything we did was gingerbread themed, tomorrow it will be snowman themed, they’re excited about it and if you try to fight it you’re probably going to have less engagement first of all, and probably more people not completing the work, that kind of stuff. So I looked on “Teachers Pay Teachers” and got some stuff off of there. I’ve gotten some stuff just from reading some other people’s blogs and things like that. We have an actual math curriculum that we don’t use, I don’t think we’ve used one thing from it this entire school year. It doesn’t allow, first of all it doesn’t align with the Indiana standards, it’s Common Core which is close but not exact, but it doesn’t allow for as much in-depth discussion that we need for them to be able to do well on our assessments. So we have just decided to kind of scrap it, if there’s something we can use from it, that’s great, but most of the time we don’t even go to it as a resource.  (Interview, fall 2015)


Here, the teacher had a specific problem that was relevant for her local context, which was to enlist student participation and keep students engaged in learning before the holiday. Further, the teacher situated her problem in a larger organizational context, which concerned the insufficiency of the curriculum. She described two characteristics of the curriculum that contributed to her general practices of going online for resource access. First, she noted the district curriculum was designed to be aligned to Common Core but not their state standards. The second reason she described was her perception that the district curriculum was not sufficient for in-depth discussion that would enable her students to do well in state assessments. These specific-general problems on portraying the content had directed the teacher to VRPs such as TpT for a solution.


INCIDENTAL CURATION


Teachers are not just teachers when they are in school. Their professional identity is part of who they are in all of their life experience (Lasky, 2005). Teachers’ online engagement may also have entertainment or personal purposes. As they navigate the online platform, however, because of who they are as teachers, and also because of the social algorithms that directly influence what content will be recommended to them based on their general activity online (Lazer, 2015), teachers will inevitably encounter educational content that may interest them incidentally. The encounter of certain instructional ideas or tasks may create a spark in teachers’ creative minds because they are thoughtful professionals in their craft. These sparks may turn into a more detailed road map linked to a long-perceived problem in their classroom, or the ideas can contribute to the formation of a perceived problem that was only ill formed, with disconnected elements in their knowledge system at the back of their mind. Whichever it is, the solution comes before the well-formed problems, and the curation of such ideas and resources is unplanned, unintentional, and, hence, incidental (Schugurensky, 2000). Such curation, however, may lead to future acquisition of knowledge and practices in a more purposeful way as it helps teachers better articulate what may be needed in their teaching. As a first-grade teacher put it, “I get ideas [from Pinterest], I get ideas, or I’ll see some part of a lesson and it will give me an idea for something else.”


In our data, however, we did not observe teachers’ articulations of specific problems of teaching as a direct result of the incidental curation. This is not surprising, given the hypothesized lagged effect of this curation process and the implicit nature of the learning outcomes as accumulations of ideas and bits of knowledge over time. We argue that as a result, there is a degree of consciousness at the time of learning in this curation process when we reconsider the informal learning theory in the context of the cloud. Teachers may recognize the ideas in a curated resource as useful for her teaching practices, but such acknowledgment may also be at a surface level. It may take a long time for a teacher to incorporate those gleaned ideas and fragmented information into her existing knowledge system for teaching. We think this may explain the phenomenon that we observed in our interview data, given that our sampled teachers are early in their career.


SOCIALIZED CURATION


Socialized curation refers to the process of a teacher being exposed to a virtual resource through communicating with a local colleague, and the curated resources may sustain even after the relationships have gone. Teachers may also indirectly access instructional resources online and curate content through the connections with their trusted colleagues whom they turn to for professional advice (Spillane et al., 2012). Essentially, all three processes may be described as socialized curation to some extent because teachers are accumulating social capital through their global networks of practice. This process specifically highlights teachers’ motives of curation as being directly influenced by those trusted colleagues in their community of practice, especially those with whom teachers talk most within the school. The socialization process connects teachers’ online behaviors with their physical networks and their particular perceived problems, as evidenced in their back-and-forth interactions with those trusted colleagues. Within our sampled teachers, we have a few instances of the socialized curation process in those schools where the grade-level cohorts work very close together. For example, when asked what resources she used in a lesson we observed during the center time, one kindergarten teacher commented,


I used a link I found on a website, um, that another teacher passed on to me of activities they had done for shapes in the past. My partner teacher actually, and she passed it along to me through a discussion that we had a couple of years ago in teacher PLC meetings. (Interview, fall 2015)


In this teacher’s narrative, she relied on the judgment of her partner teacher and trusted the website passed on by this colleague as a worthy source for accessing resources. She may not have maintained the relationship with the colleague from whom she got the resource, but she curated and enacted this particular resource as a result of direct interaction with her trusted colleague in the network.


The relationship and the exchange of resources can be reciprocal in the socialization curation: Teachers may access resources online as a collective effort through discussions and negotiations with colleagues. In our interview data, one first-grade teacher mentioned,


As a first grade we as [township name] the maps don’t align with our math series, so a lot of what we do is either teacher found or teacher made, grade level made.  So what we were using today was something that [grade-level partner’s name] in Room 2 and I had purchased a pack of teacher pay teacher last year so it was just something that we got there but it’s all just teacher found stuff. The exit tickets that they do and the stuff are all teacher made or found. (Interview, spring 2016)


In this narrative, the first-grade teacher pointed out the lack of alignment between the curriculum map and the textbook provided by the district as the shared problem of teaching within her grade-level team. To address this problem of portraying content that was aligned to the official curriculum, the teacher and her grade-level partner with whom she planned closely chose to invest in a packet of TpT resources via a collective action. What is not clear is how they came together and made a decision on what resources to curate out of their own pocket. One teacher may initiate the online resource-seeking behavior when the team has identified a shared problem they face in teaching. Alternatively, all teachers may be involved jointly in the selection process of virtual resources and discuss their implementation in different classrooms. In both scenarios, teachers’ curation of curricular materials has been facilitated and endorsed by their trusted colleagues through direct interactions. Though most of them happen within the school, the trust developed in these relationships may also be cultivated in teachers’ virtual networks in the cloud.


Still, the evidence to illuminate this curation process for specific problems of teaching is tenuous in our interview data, and we did not have observation data on the enactment of resources acquired from this curation process for the core part of the lesson. This may due to the limitations of our data, given that we chose to focus on individual teachers’ practices through one-on-one interviews and observation of their lessons. The socialization process may be better explicated in observations of teachers’ collective planning while they discuss their shared problems of teaching and curation of virtual resources to meet their local needs in those informal and formal meetings. More importantly, understanding teachers’ relationships and level of trust may offer a powerful lens for analyzing how socialization curation facilitates the flow of social capital resources from the cloud, which is not picked up by our data.


In summary, the three processes of curation are different paths that teachers may take to leverage social capital resources from their local and global networks and curate a collection of instructional resources as a result. Directly, teachers may turn to colleagues for specific advice and get recommendations to access particular resources, as in the socialization process. Indirectly, teachers may individually seek out resources from their social relationships online without active input from those ties, as in the self-directed and incidental processes. Each curation process starts and/or eventually ends with teachers’ perception of certain problems in their teaching. As well defined in the literature, these problems could be the lack of students’ engagement or the inappropriateness of mathematical tasks on certain topics, leading to teachers’ active reflection of potential solutions and their actions to implement those experiments. From analyzing the perceived problems, traditionally, teachers may seek out help from the curriculum, colleagues next door, or a coach from the district. Emerging from the development of the Internet and the expansion of teachers’ virtual networks, the sources of advice and knowledge that teachers seek out extend to the virtual space. Residing in a social continuum of physical and virtual interactions, teachers are taking initiatives to curate collections of instructional resources through their local and global network of professionals and incorporating these materials into their intended and enacted curriculum (Hu et al., 2018).


ENACTMENT OF ONLINE RESOURCES: A CASE OF MS. GONZALEZ’S TEACHING


In this section, we go into further detail on the case we selected to illuminate the reification of the self-directed curation process in teaching and how the curated resource played out in the classroom. We acknowledge the importance of different types of curation and how they may intertwine in teachers’ professional experience online. Because our data focused on individual teachers’ planning and enactment of mathematics instruction, there was less observable evidence to investigate the teachers’ psychological process (incidental curation) and the details of their collaborative activities (socialized curation process). We posit that the resources frame what teachers plan and enact in the classroom; hence, understanding the complexity of the phenomenon of accessing and enacting virtual resources contributes to the conversation of teacher professionalism and the work of teaching.


PERCEIVED PROBLEMS IN MS. GONZALEZ’S CLASSROOM


A second-grade teacher, Ms. Amelia Gonzalez, was in her fourth year of teaching and worked in a suburban Midwest classroom. The district in which she worked had purchased a Common Core–aligned commercial textbook program even though the state had phased out of the national standards. Despite the designation of the textbook, there was no requirement for teachers to use this material and/or to teach mathematics in a certain sequence as long as they addressed the scope of the state standards. As a result, Ms. Gonzalez had been incorporating different materials, including but not limited to the textbook program, to craft the actual intended and enacted curriculum in her classroom. As she sat at her desk after school and reflected on her lesson planning, she said,

 

 

I decided this year I’m going to do more hands-on and more applying of our skills. So I wanted the kids to be able to identify their coins and be able to add and subtract different amounts. So today was . . . a lesson where they had to apply it, so we went to “Mimi’s Diner,” and they had to have different questions. . . Mimi’s Diner is not my idea I totally stole it from Teachers Pay Teachers, not recreating the wheel, but it fit the purpose, they got to do different things. It’s not—every problem is the same—and so there isn’t any copying off of each other, it’s all their skills. We’ve worked a lot with manipulating the coins, so I didn’t feel like they needed to do that today. . . . So this was just another way that they could keep practicing. (Interview, March 30, 2016)


In the interview, Ms. Gonzalez described her overall teaching objective for this year and her objective of the lesson for the day. Agreement and conflict existed between the overall objective and the lesson objective to some extent. For Ms. Gonzalez’s bigger curricular goal this year, she decided to incorporate more hands-on activities and skill application opportunities for her students. At the lesson level, her goal was to select a task for students to practice two areas of content—money and addition and subtraction—without the use of manipulatives that students knew well already. Removal of coin manipulatives represented a moving away from her intention to use more hands-on activities, so other forms of engaging students were needed. In the lesson, she chose a real-world context of ordering food from a diner to fulfill the goals of having students do a hands-on activity while practicing skills.


In these narratives about planning, Ms. Gonzalez had explicitly demonstrated two different problems in her teaching—portrayal of content, and enlisting student participation. In curating the online resource, Ms. Gonzalez considered different problems of teaching simultaneously. Content-wise, she chose this packet because she wanted to better portray the two areas of addition and subtraction and working with money, which are two of the content standards in the official curriculum for students at this grade level. To enlist student participation, she wanted to create more hands-on experience for the students and enlist more student participation with a range of questions with different levels of difficulty. These two types of teaching problems also intertwined with her decision-making process in the selection, adaption, and creation of instructional tasks based on the resources. In later sections, we will unfold Ms. Gonzalez’s detailed thought processes as she integrated these two problems of teaching while curating instructional resources to devise the three-day lesson series. Although Ms. Gonzalez did not explicitly connect the resources she acquired from TpT as a way to better elicit student thinking in class, she used the activities in a way that helped her elicit some students’ thinking in the enactment, which will be discussed in a later section of this article.


We also noticed one particular characteristic in Ms. Gonzalez’s articulation of her problems of teaching. She did not explicitly connect her curations of instructional resources from virtual spaces as a way to preserve classroom order, nor did she purposefully monitor the classroom order while she “released the students.” This phenomenon was actually prevalent in our data. From observation of teachers’ mathematics lessons, we sometimes observed classroom behavioral issues, and those examples of misconduct did trouble some of our sampled teachers in the classroom. It was not surprising when a teacher did not connect her use of the designated curriculum materials to the purpose of preserving classroom order, given that those materials were developed for the academic part of school life—which is to learn content. Given the wide range of resources available in the cloud (e.g., ideas, pedagogical approaches, tasks, advice), we found this lack of attention to a well-documented teaching problem in the curation process intriguing.


SEEKING ONLINE FOR MATHEMATICAL TASKS IN PLANNING FOR THE INTENDED CURRICULUM


In this section, we delineate the curation and the planning process taken up by Ms. Gonzalez and how the two primary teaching problems she articulated played a role in her decision-making process as she prepared to teach.


Mimi’s Diner, which is one of the tasks from the TpT unit on money that Ms. Gonzalez paid $8 for, was not the only instructional task that she acquired and used for her class. Ms. Gonzalez turns to Pinterest and TpT about one to three times per month to acquire instructional resources for mathematics but never shares resources herself. In the interview, Ms. Gonzalez talked about three lessons that connect to one another and achieve the same goal of practicing addition and subtraction with money in some shopping context (see Table 1 for the task and the teacher’s intended curriculum as described in the interview on planning).


Table 1. Tasks Featured in Ms. Gonzalez’s Three-Day Lesson Sequence


Task

Teacher’s Description of Tasks

Day 1: Mitzi’s Candy Shop1

[39_23307.htm_g/00004.jpg][39_23307.htm_g/00006.jpg]

 “Yesterday we did more of a I helped and showed them and modeled a few of the problems, and so today it was just a release of “here we go, this is how you’re going to do it.”

Day 2: Mimi’s Diner[39_23307.htm_g/00008.jpg]

[39_23307.htm_g/00010.jpg]

“They knew how to get around the room, I added more to their plate than yesterday, yesterday they did eight problems, today I wanted them to try all 15, and most of them did. I [teacher paused]. . . also today, the problems are a lot different today, it’s exactly this amount, it’s, two ways to find this number, so it was more than yesterday.”

Day 3 Grocery Shopping[39_23307.htm_g/00012.jpg]

“Well tomorrow is going to be the full release, so I have, they’ve brought in like grocery store clippings so they will be spread out. I’m going to give each of them a grocery list with, it’s blank but they will each have a different amount that they can spend, that way it’s not “Oh hey how’d you make your $20?,” it’s going to be different. So they can pick, I haven’t decided if I’m going to have them cut out the item or just write things down. Some of my students have really bad handwriting, so I’m not quite sure if I’ll be able to read it, but my vision is that they cut it out, write what they’re buying, and then they have to keep subtracting to get that total or then add it up and see what they’ve got.”


1 Three stars on the task card means enrichment problems. There are also one-star and two-star  problem cards for differentiation.


In developing a sequence of lessons, Ms. Gonzalez selected two activities from the virtual resource packet that she bought for $8 for the first two days and created a related activity in the real grocery shopping context for the third day. In the process of considering which instructional task to use in class, the teacher considered two types of complexity across the three-day lesson sequence: the students’ agency level, and the content variation and differentiation. On one hand, to increase students’ agency level in practicing skills, Ms. Gonzalez began the lesson sequence by modeling most of the problems on Day 1 and then released students to work on the Mimi’s Diner task, which featured problems similar to those she modeled the day before. She also expected students to finish more problems on Day 2 as part of the goal of getting better at the skills. The teacher considered Day 3 to be the students’ full release; they had to bring their own clippings and decide themselves what they were going to shop for. They were asked to create a shopping list with groceries and calculate the total amount and the change left as the final product of the lesson (see Day 3 task image in Table 1 for an example of student work). On the other hand, to vary and differentiate the content, Ms. Gonzalez focused on different ways to practice addition and subtraction with money. Day 1 was more about adding the prices of two or three items purchased, whereas Day 2 involved two different ways to buy things that would add up to a given exact amount. Day 3 involved both addition and subtraction explicitly; students not only needed to add all the items purchased, but they also had to figure out the change left and make sure they did not overspend. These two complexity types across the lessons provide us with an understanding of this teacher’s selection of instructional tasks and the adaptation she made to extend the virtual resource that she accessed from TpT. Additionally, the complexity in her planning also demonstrated her considerations of the two teaching problems—portraying content and enlisting student participation—as integral parts of the learning experiences that she devised for students.


TEACHING WITH MIMI’S DINER IN THE MOMENT FOR THE ENACTED CURRICULUM


In the enactment of the online resource, how Ms. Gonzalez set up the activity and what she was doing with students are largely framed by the task itself. As she reflected on the planning, one of the purposes of selecting this task was that students could not copy from each other; it was an open-ended task in the sense that the money that had to be paid for the meal and change received depended on the food item(s) that students chose to order. As a result, Ms. Gonzalez set up the activity as individual work, and she sat with two students at a table to help them navigate the tasks. Although not explicitly mentioned in her interview, Ms. Gonzalez’s work with these two students who needed additional help presented another perceived problem in teaching, and how she could address particular students’ needs was made possible by the nature of the task and the activity structure that the task required to be enacted.  


The teacher’s interactions with the two students were largely procedural at first; the initial question cards (see Day 2 task in Table 1) for Mimi’s Diner only asked students to find out how much a dinner meal cost without specific cost requirements. Ms. Gonzalez focused on having the two students work independently, and she spent most of the time talking about how to perform a standard addition algorithm with different money amounts in decimals. As the questions on the cards became more open-ended and required students to spend no more than a certain amount, the tasks afforded the teacher more opportunities to make the real-world connections for the students. Ms. Gonzalez’s interactions with students were still largely teacher-driven in nature throughout the lesson. But with these question cards, she made a great effort to engage students in checking the plausibility of getting certain food items in order to make connections between the mathematics procedures and real-life situations. An example of these interactions is demonstrated by the following excerpt:


Teacher: Well it says for a combo meal and a dessert. This is 3 desserts. So we need a combo meal, which is a meal with a drink and a dessert. How much money do you have to spend?


Student: $3.00.


Teacher:  $3.00, so write $3.00 on your board.


Student writes $3.00 on her board.


Teacher: So you have $3.00 to spend. You can spend it on a combo meal and a dessert. Can you point to a card that you could not use?


Student points to a food item.


Teacher: Why could you not use this one?


Student: Because its $3.50 even and you need a dessert.


Teacher: Right, and so if you already spend. This is already overspending. Right?


Student: Yeah.


In the remainder of the lesson, as Ms. Gonzalez took turns to help the two students work through different question cards, the conversations around plausibility of purchasing the food largely contributed to the connections between the procedures and the real-life context for the mathematics instruction. Selecting this task, Ms. Gonzalez used a familiar problem context to provide mathematical affordances for students with differing prior knowledge in order to access the content and engage with the mathematics in a real-world scenario. The interactions, however, were more teacher oriented and hence lowered the agency that students may have to elaborate on their reasoning. By working extensively with these two students, Ms. Gonzalez had demonstrated her effort to elicit student thinking. Specifically, she attempted to help these two students reason about the real-world context and used their contextual knowledge to make sense of the addition and subtraction word problem. At the same time, as Ms. Gonzalez chose to work with these two students based on her analysis of student needs, the enactment of this task may also have created another dilemma: attending to the potential learning needs of other students in the class.


As an early-career teacher, Ms. Gonzalez may not be “perfect” in her mathematics instruction. Her planning and enactment of mathematics, however, were deliberate. She had to choose specific instructional tasks and coordinate among her overall and lesson objectives across days to manage the perceived problems of teaching. When she selected instructional tasks with various access points to the mathematics and differentiated mathematics problems, she opened up the possibility for students to engage with different ways of practicing addition and subtraction, either independently or in groups as framed by the setup of the task. When she situated the mathematics in different shopping contexts across days, she anticipated higher student engagement with the content. When she removed the use of money manipulatives from the activities, she emphasized practicing learned algorithms in addition and subtraction while maintaining a hands-on component through the use of an open-ended real-world context. Her planning efforts culminated in Day 3 of the lesson sequence, reaching a medium or medium to high rating in the four aspects of her teaching quality, as captured by the observational protocol we used. In sum, in this example, Ms. Gonzalez is deeply engaged in her practices as an active problem solver who turned to virtual spaces for resources in her work of teaching.


LIMITATIONS: TOWARD INCONVENIENCE SAMPLING


The limitation of this study lies mostly with the sample and the way we observed teachers’ practices. In this section, we specify in detail who was in our sample of teachers and who they can represent or not represent. In addition, we delineate whether teachers outside this sample may change some of the phenomena we observed in this study, and we discuss what implications the inclusion of these observations or perspectives has for our storyline.  


As described in the Method section, our larger sample consists of K–5 teachers who are in their first four years of teaching in public schools across three Midwestern states. As generalist teachers in elementary schools, they are not just teaching mathematics in their everyday life. They need to allocate their limited time and resources to plan for different subjects and face similar and different problems across and within these areas of content in their classrooms. Because they are considered early-career in their profession, they also receive various degrees of support and professional development from their grade-level cohort, school, and district. These supports may influence their practices, forcing them to conform to or move away from particular routines, including, but not limited to, their use of online resources. On one hand, the diversity of the district backgrounds and the curriculum requirements where these teachers come from provides us with the confidence to argue for the prevalence of the use of online resources, especially those beyond the official curriculum’s purview. On the other hand, we cannot use this sample to generalize to secondary teachers and assert that they would use social capital resources in a similar way to our sampled teachers. As specialist teachers in secondary levels, the ways that secondary teachers conceptualize curriculum and curation of instructional resources may follow a completely different mechanism and manifest in different practices in enactment. In addition, how K–12 teachers who have more experience in the profession may use and teach resources obtained from the cloud is not within the scope of this study. Future examinations of different populations of teachers can add rich narratives to the phenomenon of leveraging instructional resources from cloud to classroom and help educators understand how they may impact student learning.


At the front end of this article, we cited many pieces of empirical evidence to support the basic fact that we have presented: Teachers are turning to virtual spaces and social media such as Pinterest to acquire resources. Existing data outside of this project on teachers’ use of online resources tend to focus on resource acquisition; policy reports, such as the national survey conducted by RAND (Opfer et al., 2016), was only invested in finding out what kind of curricular materials teachers used rather than how those resources were acquired and enacted by teachers. The latter phenomenon, however, may have more implications for policy makers because it will help higher level organizational units diffuse worthwhile instructional messages and knowledge to teachers in a more efficient way.


Through our survey administration, we attempted to understand the resource flows in social networks by asking whether our sampled teachers acquired and/or shared online resources they found in social media and other VRPs. However, our previous study with all participating ECTs from the larger project showed that nearly 80% of sampled teachers emphasized resource acquisition, whereas only about one fifth also reported sharing online resources (Hu et al., 2018). The sampled teachers we focused on in this study also indicated the same pattern in using social media, as suggested by the subset of the survey data. As we conceptualized the curation of curriculum in these spaces, we thought of it as a process of accrual and exchange resources in networks. Because this group of ECTs mainly engaged in resource-acquisition activities, we did not investigate how teachers may play other roles in their local and global social relationships. For example, teachers, especially those more experienced in their profession, may serve as transceivers of resources in their networks, having their instructional resources shared and accessed widely by other teachers (Supovitz et al., 2017). The different directions of resource flows in these social relationships, the explaining factors of these paths, and the resulting implications are not the main focus of this study, but they are of great importance if we want to systematically specify the mechanism of social capital among teachers and from cloud to classroom.


DISCUSSION AND CONCLUSION


At the core of this study, we see teachers taking up their agency and drawing on a particular type of social capital resource to manage their enduring problems of teaching. The line between the formal curriculum materials provided by districts, such as textbooks, and the informal curriculum, such as instructional tasks found within Pinterest, is less clear than many educators may imagine. In some districts where teachers themselves put together a curriculum tailored to their local contexts by discussion and negotiation, the resources attained from the cloud may be incorporated into and adapted as part of the “designated curriculum,” as conceptualized in Remillard and Heck’s (2014) framework of curriculum. One example of such district is the San Francisco Unified School District (San Francisco Unified School District Math Department, n.d.). Seeing the curation of instructional resources online as an integral part of teachers’ intended and enacted curriculum can contribute to a more comprehensive picture of teachers’ professionalism and the inherent work. We identified the different paths that teachers’ social capital may travel and accrue, and we argue for the importance of the community of practice online in the facilitation of resource flow from the cloud to the classroom. Also, we used a teacher’s planning and enactment of instructional resources obtained from the cloud for a three-day lesson series as an example to demonstrate how these curations and perceptions of teaching problems can culminate in a teacher’s actual practice and impact her students in mathematics learning.


In this article, many of our ECTs drew on instructional resources accessed from VRPs as the social capital resource to solve particular teaching problems. We often observed teachers’ curation of instructional resources from the cloud as ways to help them better portray content, enlist student participation, and elicit student thinking. Teachers may have to consider multiple teaching problems simultaneously in their planning and enactment of the resource, and our data showed that they often did so. Additionally, teachers may not plan for addressing certain teaching problems explicitly as they reflect on their practices, but their enactment suggests their attention to the problem; we saw this in the case of Ms. Gonzalez as she elicited student thinking by working with two students and asking prompted questions to have them make sense of the word problems in a real-world context. It could be that the teacher could not well articulate all the problems that she simultaneously managed in her mind. Alternatively, it could be that the teacher saw an opportunity during the instruction and decided to take on more of her endemic teaching problems. To understand more about the complexity of managing the teaching problems in planning and in enactment, we would need to collect more qualitative data on teachers’ decision-making processes about their teaching moves and to triangulate, which is beyond the scope of this study. Another interesting finding from our analysis is that teachers tend not to attend to the teaching problem of preserving classroom order directly and explicitly across their curation processes. Future studies may further examine the relationships among the modes of curation, the types of resources acquired, and the uses of these resources for each of the persistent problems that teachers face in their everyday lives.


The process of accessing the instructional resources, as delineated in the three modes of curation, demonstrates the complexity of the social network and social capital accrual mechanism in the 21st century, when teachers’ professional communities expand beyond the school walls. Previous researchers have argued that teachers are social beings, and their behaviors are facilitated or constrained by the resources available in their social networks (Bidwell & Yasumoto, 1999; Granovetter, 1983). We also want to echo these ideas and highlight the influence of virtual spaces on teachers, which is still largely understudied. As teachers actively curate instructional resources online in their routines, it would be unwise for researchers and policy makers to completely disregard teachers’ agency in this space and the potential of those social capital resources therein. Teachers, even those who were considered early-career professionals, have worked diligently to construct meaning around their practices and the classroom by making sense of their students’ needs and curricular gaps to address those needs (e.g., Christou et al., 2009; McGinnis et al., 2004). As teachers resort to social capital resources within the school and beyond—from their school-based colleagues and global community members in physical and virtual spaces—they are leveraging social capital to inform their practices.


Our work presents the considerations and thought processes of teachers’ curation of instructional resources within virtual spaces and enactment of the resources. There are many layers in teachers’ planning and teaching as they use the social capital resources they acquire online. Teachers may consider the portrayal of content that may be covered in assessments or pacing guides. Teachers may contemplate ways to use these resources effectively in certain activity structures to maximize students’ participation, while at the same time eliciting students’ thinking in order to gauge their mastery of content. What is more, as demonstrated by Ms. Gonzalez in this article, teachers may envision a trajectory of learning experiences for their students and adapt and even construct instructional tasks based on the online resources acquired. The complexity of the mathematics instruction over the lesson trajectory positions teachers as active problem solvers who are able to leverage a variety of resources beyond the formal organizational context in their craft.


The combination of social capital resources and classroom processes in this study provides the foundation for researchers with different perspectives to further investigate the emerging phenomenon of social media and education. Our findings, however, may lead to more potential areas to be explored than discovered. As discussed in the Limitations section, the teachers we interviewed and observed were mostly in their first four years of teaching at K–5 levels. Future studies may investigate the interaction between mechanisms that facilitate teachers’ access to and sharing of instructional resources and how teachers leverage social capital resources from virtual spaces. These effects may differ based on each teacher’s experience, grade level, and school culture. In another work in this special issue (Liu et al., 2020, this issue), we have begun to tap into the instructional resource flows as a way to understand the influence of teachers’ network ties on their practices, and how tie strength results in differentiated access of certain instructional resources. By examining what we conceptualize as the socialized process of curating instructional resources with the social network approach, we can further make sense of the particular influences of different types of physical and virtual colleagues on the intended and enacted curriculum in the classroom.


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Cite This Article as: Teachers College Record Volume 122 Number 6, 2020, p. 1-33
https://www.tcrecord.org ID Number: 23307, Date Accessed: 12/6/2021 6:57:54 PM

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About the Author
  • Sihua Hu
    Northwestern University
    E-mail Author
    SIHUA HU is a postdoctoral fellow on the COHERE project at Northwestern University. Her research examines various dimensions of teaching quality and how teaching quality is related to mathematics teachersí social networks within physical and virtual spaces. Dr. Hu earned a PhD in mathematics education from Michigan State University and was a co-PI for an American Education Research Association conference on social media and education, convened in October 2018.
  • Kaitlin Torphy
    Michigan State University
    E-mail Author
    KAITLIN T. TORPHY is the lead researcher and founder of the Teachers in Social Media project at Michigan State University. Dr. Torphy was a co-PI and presenter for an American Education Research Association conference on social media and education, convened in October 2018 at Michigan State University. She has published work on charter school impacts, curricular reform, and teachersí social networks, and she has presented work regarding teachersí engagement within social media at the national and international levels. Dr. Torphy earned a PhD in education policy and a specialization in the economics of education from Michigan State University in 2014 and is a Teach for America alumna and former Chicago Public Schools teacher.
  • Kim Evert
    Middle Tennessee State University
    E-mail Author
    KIM EVERT, Ph.D., is an assistant professor in the Womack Educational Leadership Department at Middle Tennessee State University. Her research examines how leadership, professional development, and school context shape teaching practice and teachersí perceptions of their work.
  • John Lane
    Michigan State University
    E-mail Author
    JOHN L. LANE is an outreach specialist at Michigan State Universityís Office of K12 Outreach. His research focuses on multiple aspects of reform, including teacher learning, social contexts of teaching, school leadership, and policy. His recent research on teacher evaluation policy was published in the American Educational Research Journal. He has also recently published articles on teacher social networks in the Elementary School Journal and the Journal of Educational Change and on the enactment of virtual resources in Teachers College Record.
 
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