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UNDERSTANDING MATHEMATICS TEACHER BLOGGING: AN INITIAL FORAY INTO THE MTBOS Judy Larsen Simon Fraser University Many mathematics teachers around the world are engaging autonomously in the practice of blogging, where teachers write publicly about their teaching experiences. Investigating this phenomenon may illuminate aspects of mathematics teachers’ daily practice for which blogging serves a purpose. Such aspects may be useful for the mathematics education community in its efforts to improve mathematics teaching. With the global aim of investigating the teacher blogging phenomenon, this preliminary investigation attempts to characterize particular ways in which mathematics teachers blog by using a grounded theory approach. The resulting categorization of ways in which teachers blog may prove useful as a mechanism for identifying roles of various bloggers in the Math Twitter Blogosphere (MTBoS) in further studies. INTRODUCTION More and more mathematics teachers are engaging in the Math Twitter Blog-o-Sphere (MTBoS). The MTBoS is a set of mathematics teacher bloggers who blog regularly about their teaching practice, and connect over Twitter under the hashtag #MTBoS. Currently, there are over 600 identified mathematics teacher blogs in existence (Meyer, 2014), many of whom connect via the #MTBoS hashtag. This relatively recent technological advancement has afforded teachers the opportunity to share about their practice at a global scale more easily than ever before. Teachers are publicly posting their resources, writing about their daily practice, and sharing their dilemmas. The public nature of blogs allows for teachers to connect with like-minded teachers, with whom they can communicate about their teaching practices. What’s interesting, is that these mathematics teachers do not blog in response to course requirements or external prompts, but rather, they blog in response to their experiences as mathematics educators. These teachers clearly spend many hours blogging with no compensation and no mandate. This self-directed, self-guided, and self-funded teacher activity is a rich phenomenon of interest that may provide insight into the nuances that many mathematics teachers seek when striving for success in their practice. Ironically, this phenomenon is largely unstudied. In mathematics education, empirical investigations related to blogs are limited to studying the use of blogging as a treatment within either a mathematics course (Nehme, 2011), or a mathematics education course (Silverman & Clay, 2009). These studies do not account for the autonomous and self-driven nature of the blogosphere. In science education, there has been some development in this direction by Luehmann (2008), where one year’s worth
Larsen of one particular science teacher’s blog posts were analysed with the purpose of determining the teacher’s identity development. In general education literature, there is also a focus on looking at blogging as a mechanism for learning enhancement (Deng & Yuen, 2011). However, there is no clear work being done in mathematics education in response to this recently emerging phenomenon. As such, the preliminary study outlined in this paper aims to unpack some of the manners in which mathematics teachers are currently engaging in the MTBoS, with a particular focus on blog posts. Determining a characterization for the ways in which mathematics teachers blog can give insight into what the blogging environment has to offer for these teachers, and can form the basis of future work on the phenomenon of mathematics teacher blogging. METHODS With the overall aim of this preliminary study being to determine ways in which mathematics teachers blog, it implies the need for analysing a selected variety of blog posts. Since the number of blog posts made by mathematics teachers worldwide is astronomical, it is impossible to be exhaustive. Rather, a manageable number of mathematics teacher blog posts were selected for this preliminary investigation with the intent of choosing blog posts to represent as wide of a variety as possible. Blogs selected included those managed by Julie Ruelbach, Kate Nowak, Sarah Hagan, Katenerdypoo, Sam Shah, Shawn Cornally, and Maria Kerkhoff. These bloggers were chosen for the variety in number years for which they have been blogging, amount of detail they provide in their posts, and the nature of the content they typically publicize. A sample of blog posts from these teachers were selected as data in order to capture as broad of a spectrum of mathematics teacher blog posts as possible. During blog post selection, a convenient source of data was discovered, where one blogger (Nowak, 2013) asked her followers why they blog. Nowak’s (2013) intent in publicizing this query was to prepare herself for a presentation where she would share about the practice of blogging in a mathematics teacher context. In her post, she asked teachers why they started engaging in the Math Twitter Blog-o-Sphere (MTBoS), what keeps them coming back, why they write, what they get out of it, and what they would like to get out of a talk on blogging. Over 50 mathematics teachers from across the world provided responses, and these responses formed the first portion of the data set for this study. This opportunistic data set included many statements by mathematics teachers where reasons for blogging were made explicit. Although Nowak’s (2013) query was primarily about why her followers blog, and not about ways in which they blog, responses were more suitably interpreted as ways in which they blog. This is because it is impossible to determine why someone does something without having an in-depth discussion with them in person. If a blogger writes that they blog ‘to share their work with others,’ this is treated as a manner in which they blog rather than an implicit reason for which they blog. Hence, the data set
Larsen was analysed for the ways in which teachers blog. Guided by principles of grounded theory, two rounds of coding were performed on this data set. The codes generated from the responses to Nowak’s (2013) blogging reasons query were then used in the analysis of the data set of blog posts selected where reasons for blogging were not made explicit. In these posts, the manners in which they blog were identifiable. Each post was analysed according to the previously generated codes, with new codes being added when necessary. Recursive coding was performed until themes emerged. These themes were used to develop categories that characterize different ways in which mathematics teachers blog. RESULTS The analysis reveals the various ways in which mathematics teachers can engage in the practice of blogging in relation to their practice. In particular, the following themes emerged from the data as ways of interacting in the MTBoS: collecting, documenting, reflecting, and connecting. It was also found that these themes can work together to create categories with which further blog posts can be characterized. I will first overview these themes and what they refer to in the context of blog posts made by mathematics teachers, and then I will overview how these themes can work together to provide a method of categorizing blog posts. Collecting One theme that emerged from the blog data was the idea of collecting. Teachers seem to be using their blog spaces to collect resources that they find interesting or that they would like to use in their classrooms. For example, Julie Ruelbach has a list of resources that she has gathered by lurking through other blogs. Another example of this is Sam Shah’s virtual file cabinet. However, some bloggers use their blog posts or their Twitter account to collect resources. For example, Katenerdypoo (2014) makes a post about an idea she acquired from another blog regarding the use of a counting circles strategy to teach fractions. She notes how she plans to use it in her classroom with polynomials rather than fractions. In this post, Katenerdypoo writes, “I want to integrate these Counting Circles into my class not only to work on number sense, but to work on more complicated things as well” (Katenerdypoo, 2014, para. 3). In this way, she has stored the idea on her blog, which is now an easy place for her to access. Twitter, a microblogging platform, also allows users to collect interesting ideas by using the ‘favorite’ button. Users can then look at only their ‘favorite’ posts, which often include links to blog posts. Users can view ‘favorites’ lists of other users as well. Such collections of resources can aid in improving efficiency in lesson planning as well as create a source of inspiration for improving one’s own practice. Resources that are collected most often include problems, tasks and classroom strategies. They are primarily a result of lurking through other blogs and gathering interesting ideas, but they can also be collections of the blogger’s own ideas. In making a post, a blogger is
Larsen essentially collecting the idea they are writing about. Therefore, collecting may be seen as a necessary and implied aspect of blogging. Documenting Another necessary and implied aspect of blogging is found in the documenting theme. Essentially, through writing a blog post, bloggers are documenting in detail either something they have tried or something they have thought of. The key distinction between collecting and documenting is that bloggers who document are contributing their own unique experience or perspective. Many bloggers use various media sources to exemplify in detail their experiences and thoughts on teaching and/or doing mathematics. Bloggers’ experiences or ideas become reified through writing and can be then referred back to. This forms a good starting point for bloggers to begin reflecting on their practice. In fact, reflection often occurs in the midst of documenting, but is not a necessary result. For example, Sarah Hagan (2012) makes a post about her experience in implementing an interactive notebook strategy while teaching linear equations. She spends the first part of her post detailing the activity systematically, making sure to include photos of student work. She includes files of the handouts that she used. She also provides clear reasoning for the choices she made in setting up the activity. An example of this is when she writes, “I knew some of my students would benefit from actually manipulating the pieces of the equation” (Hagan, 2012, para. 8). She also makes note of struggles that she came across such as how time-consuming it was for students to cut out and glue equation pieces in their interactive notebooks. At the very end of her post, in the last paragraph, she writes a short reflection on the activity. It may not have been the most effective use of time in my classroom, but it was not a waste of time. The experience has made me a better teacher. No, that is not true. Reflecting on the experience has made me a better teacher. (Hagan, 2012, para. 13)
Documenting her experience led her towards reflecting on the experience. However, the reflective piece does not necessarily accompany a documentation. For example, Sarah Hagan (2014) has another post where she strictly presents posters that she has put up in her mathematics classroom. In this example, she is purely documenting. Reflecting As mentioned, documenting experiences and ideas can lead to reflecting on those experiences and ideas, and reflecting came out of the analysis as one of the key themes. So reflecting is an extension of the documenting theme, where some bloggers add meta-level comments to show self-assessment and self-awareness of practice. This often leads to goal setting. For example, Shawn Cornally (2014) posts about a napkin folding problem he gave his students. He documents the problem and how it was used in his classroom, but provides meta-comments that show he has reflected on the experience. He notes that he abided by all stages of “good math problem solving,” but questions if this is really the point.
Larsen I mean, if we claim that teaching math is really an exercise in critical thinking (which is the most sophist word in education today, btw), with the stated goal of exercise being to create muscle memory, efficacy, and future extensibility, I have to wonder what would happen if you actually assessed a student before and after a math course if you’d see any change in the critical-ness of their thought. (Cornally, 2014, para. 10)
At the end of his blog post, he provides a self-assessment on his approach to the described teaching scenario claiming that “what [he] missed was climbing up to [the] abstraction correctly” (Cornally, 2014, para. 22). He ends with options for improvement, noting that he is “going to have [his] students take the rectangle problem and count squares first, even though that somehow offends [his] adult math brain” (Cornally, 2014, para. 28). It is evident that there exist various degrees of reflecting. Although it is out of the scope of this preliminary investigation, future work on analysing degree of reflection in a blog post may be informed by literature on reflection. In particular, Van Manen’s (1977) hierarchical representation of levels of reflection (technical, practical, and critical), or Scanlon and Chernomas’ (1997) three stages of reflection (awareness, critical analysis, and new perspective), or Wong et al. (1997) and Kember et al.’s (1999) three levels of reflection (non-reflectors, reflectors, and critical reflectors) are worth considering as frameworks for determining reflectiveness. Literature on metacognition (Flavell, 1979) can also inform this aspect of blogging. Connecting Another emergent theme in blog use is that of connection. Unlike journals, blogs are public, and therefore allow for connection among members to occur. Connecting can begin with the process of collecting, or even that which precedes collecting, which is lurking through other bloggers’ resources. In collecting resources and ideas from others, bloggers find sources of inspiration. They may become drawn to these sources of inspiration and begin to interact with them. For example, they may find a resource, change it slightly, and repost about their experience with it. More importantly, they may document their experience and put out a call for help with how to resolve an issue they are having. In this way, they are drawing on the community of mathematics teacher bloggers that they have collected. A good example of this two-way interaction is Kate Nowak’s (2009) post on her introduction of right angle trigonometry. She begins by writing, “I am conflicted every year about how to introduce right triangle trig to my Algebra 1 classes” (Nowak, 2009, para. 1). She documents her approach in detail, and then writes about what she is having troubles with. I keep trying this lesson every year, because I really want it to work. I really think it should work. Part of the problem is that we run out of time. I can't get this whole thing done in 43 minutes, and there isn't really a good point to stop and pick up the next day. The next day, I just tell them "SOHCAHTOA" (*huge resigned sigh*) (at least I don't claim Sohcahtoa was a Native American princess) and start teaching procedure. And feel like I am committing malpractice, and stealing my paycheck. Help. (Nowak, 2009, para. 10).
Larsen Her post initiates a discussion in the comments section, and she later posts an update stating that she has “revised [the] activity based on the comments and discussion on [the] post” (Nowak, 2009, para. 11). She provides a link to a new blog post that describes the revisions. Kate is capitalizing on the community of followers she has attracted here and is able to connect with the MTBoS to inform her practice. This is the ultimate scenario of connecting. However, there are partial manifestations of connecting that occur within other posts. Namely, connecting refers to whenever a blogger not only collects ideas for their own use, but reaches out to the readers by asking for help and seeking feedback or by building on the work of others and contributing to the needs of the community. These types of connections are particularly sought after by teachers who are in isolation. For example, in a response to Nowak’s (2013) inquiry about why bloggers blog, one blogger responds by addressing this very notion. I blog to share. I spent my first years of teaching in isolation, knowing I was reinventing the wheel, but not knowing where to find all the other inventors. Then I was introduced to this amazing online math community (by you and Sam and Ashli) and now I want to give at least as much as I take. I hope to help new teachers feel less like they're drowning as they try to plan every lesson and to get feedback from teachers of all experience levels. I want to continue to grow in my practice and the reflection I do as I both read and write plays a major role in that growth. (Tina Cardone’s response to Nowak, 2013)
Although determining degrees to which bloggers connect is out of the scope of this investigation, it should be noted that further work on developing such a scale can be informed by literature on communities of practice (Wenger, 1998) and legitimate peripheral participation (Lave & Wenger, 1991). Towards a theory The themes developed and outlined in the preceding paragraphs (collecting, documenting, reflecting, and connecting) can be integrated to provide a way of categorizing mathematics teacher blog posts. In particular, documenting and reflecting can form opposite poles of one axis because documenting is the entry point towards reflecting, as exemplified by Cornally’s (2014) post. One needs to first document something in order to effectively reflect on it. Levels of reflection can be developed by looking more closely on literature on reflective practice and metacognition. Similarly, collecting and connecting can also be seen as opposite poles of another axis because collecting can be seen as an entry point into connecting. This is exemplified by Nowak’s (2009) post. Before one connects with others, they need to collect sources that they find worth connecting with. Levels of connecting can be further informed by literature on communities of practice. Overall, a field may be developed to capture the various categories of engagement in the blogosphere by mathematics teachers (see Figure 1 below). For example, Nowak’s (2009) post could be categorized as being in the top right hand quadrant because in it, she is reflecting and connecting. Such a field for categorization will be useful in future work on this phenomenon because it can provide a mechanism with which to identify a larger sample of data.
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Figure 1: Field of Blogging Reasons The framework developed here recognizes that bloggers can enter the MTBoS through collecting and documenting in their posts, but have the opportunity to grow in the MTBoS through varying degrees of reflecting and connecting. In his response to Nowak’s (2013) query about mathematics teacher blogging, one blogger writes, “Before blogging, I had never truly "reflected" on my practice and over the year, it became a part of my professional growth” (Kyle Pearce’s response to Nowak, 2013). Another blogger responds, “I keep coming back for two reasons: growth and community” (Wendy Menard’s response to Nowak, 2013). And finally, another response captures the cycle of growth within the MTBoS. Content is always marinating in my brain. If I have to put pen to paper, it forces realizations. I write to flesh out my own thoughts, to ease the mental friction. If I have to put down a coherent flow of ideas, then I have to make sense of what I believe. Writing forces me to develop my own thoughts. I’m always thinking about math teaching and math learning. I owe the MTBoS for the increase. As a result, I’ve also started thinking about learning and schooling in general, in any subject. That’s good for students and for me. (John Berray’s response to Nowak, 2013)
Therefore, it is evident that the MTBoS has the capacity to be a valuable resource for mathematics teachers. Determining more specific conditions that encourage entry into this practice and identifying particular elements of the practice that make it worthwhile for teachers of mathematics could further inform the field of mathematics education in its efforts at improving mathematics teaching and learning. CONCLUSION This preliminary investigation of how mathematics teachers engage in the practice of blogging has been fruitful in developing a categorization of ways in which mathematics teachers blog. This categorization can form a launching point for further study. In particular, the categorization can be used as a lens to identify additional mathematics teacher blogs for further investigation. It may also prove useful in identifying teachers’ roles in the MTBoS community. Future directions include determining the benefits that teachers experience based on the ways in which they blog.
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