Rationale for Study/Purpose Statement
Student teaching is a pivotal opportunity for learning to teach under the guidance of mentors (Feiman-Nemser & Buchmann, 1987; National Council for Accreditation of Teacher Education (NCATE), 2010; Wilson & Ferrini-Mundy, 2001; Zeichner, 2002). Research reveals a vast array of mentoring relationships differentiated by the nature and frequency of communications between student teachers and their mentors (Hawkey, 1997; Odell & Wang, 2002). Several studies link the contents of conversations between student teachers and their mentors to student teachers’ learning and practices (Bennett, 2010; Blanton, Berenson & Norwood, 2001; Hawkey, 1988; Nilssen, 2010; Wang & Odell, 2002, Wang & Paine, 2001). Student teaching presents an opportunity for
university supervisors to help mathematics student teachers connect theory with practice by implementing standards-based instructional practices. Generally, university
supervisors visit student teachers only a few times throughout the semester to observe and provide feedback about student teachers’ practices. Consequently, university supervisors’ efforts to mentor student teachers toward standards-based instructional practices may be hindered by the limited occasions of mentoring conversations with student teachers (Borko & Mayfield, 1995; Frykholm, 1996; Richardson-Koehler, 1988). Furthermore, unlike cooperating teachers who are on-site, university supervisors are often disconnected from the context of student teachers’ day-to-day experiences that could serve as catalysts for discussions about standards-based instructional practices. Online
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social networking provides an opportunity for consistent communication between university supervisors and student teachers about student teachers’ daily experiences. Thus, online social networking is a potential venue for university supervisors to facilitate student teachers’ understanding and implementation of standards-based instructional practices that are grounded in their authentic student teaching experiences. The purpose of this study was to explore the potential of online social networking as a venue for mentoring secondary mathematics student teachers toward standards-based instructional practices.
Definition of Terms Standards-Based Mathematics Instruction
The National Council of Teachers of Mathematics’ Principles and Standards for
School Mathematics (NCTM, 2000) outlines the essential components of “high-quality”
and “engaging”, mathematics instruction” (p.3). In particular, the six principles for school mathematics (Equity, Teaching, Assessment, Learning, Technology, Curriculum) and the five process standards (Communication, Problem-Solving, Connections, Reasoning and Proof, and Representation) are the over-arching themes that inform the classroom practices that compose standards-based mathematics instruction (NCTM, 2000). The over-arching themes of standards-based mathematics instruction are echoed in Wang and Odell’s (2002) description of standards-based teaching practices across all disciplines Wang and Odell (2002) assert that standards-based instruction is manifested in teachers that
stress the importance of students’ deeper understanding of concepts and
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and theories; challenge students’ misconceptions and connect students’ learning meaningfully with their personal experiences and real life context; place students’ ‘active discovery’ of important ideas at the center and encourage students to share and examine what they find through discourse and; strive to teach all students and promote excellence for students whatever their gender, race and social, cultural, and economic backgrounds (p. 484).
For this study, the researcher synthesized Wang and Odell’s (2002), cross disciplinary description of standards-based instruction with NCTM’s (2000) vision for teaching mathematics to define standards-based mathematics instruction as consisting of the following teacher actions:
elevating conceptual understanding and surfacing “ big’ mathematical ideas,
eliciting and attending to students’ mathematical thinking,
connecting mathematics to real-life contexts,
using and connecting a variety of representations,
facilitating active discovery and mathematical investigations,
promoting student collaboration and mathematical discourse and,
attending to equity in mathematics instruction.
This definition of standards-based mathematical instruction serves to characterize and delineate aspects of standards based instruction so that they can be easilyidentified and explored in the context of this study.
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Mentoring Toward Standards-Based Instruction
Case study literature where mentors influenced novice teachers’ learning to teach in ways consistent with standards-based teaching suggests that mentoring student
teachers toward standards-based instruction involves purposefully and consistently using specific teaching events as the catalysts for (a) engaging student teachers in reflection and dialogue about their beliefs, subject matter knowledge, and developing practice (b)
challenging student teachers to reinterpret and reexamine teaching events in light of standard-based teaching practices and (c) offering specific suggestions and reasons for standards-based practices to be implemented in student teachers’ current practice (Bennett, 2010; Blanton, Berenson, & Norwood, 2001; Nilssen, 2010; Wang & Odell, 2002; Wang & Paine, 2001; Wang, Strong, & Odell, 2004). In this study, the university supervisor/researcher will employ the processes described above to mentor student teachers toward standards-based instruction.
Research Questions
1) What is the contentof mentoring secondary mathematics student teachers for standards-based instruction in an online environment?
a) What is the content of mentoring in an online environment in relation to the following aspects of standards-based instruction:
elevating conceptual understanding and surfacing ‘big’ mathematical ideas
eliciting and attending to students’ mathematical thinking,
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using and connecting a variety of representations,
facilitating active discovery and mathematical investigations, and
promoting student collaboration and mathematical discourse,
b) What mentoring processes emerge when mentoring secondary student teachers toward standards-based instruction in an online environment?
2) How are online comments and mentoring conversations related to mathematics student teachers’ developing conception of standards-based teaching practices? (Online
mentoring conversations are defined as segments of online communications that include at the minimum, a student teacher’s initial blog post and a response from the university supervisor. In addition, mentoring conversations could include follow-up responses from the student teachers or the university supervisor.)
a) What do mathematics student teachers’ online comments reveal about their developing conception and implementation of standard-based practices? b) How are mathematics student teachers’ self-reported conception and implementation of standards-based instructional practices related to online mentoring conversations about standards-based teaching?
Rationale for Research Design
For this study, a collective case study research design was used to investigate the phenomenon of online mentoring toward standards-based mathematics instruction. A case study is an “in-depth exploration of a bounded system (e.g. an activity, event, process or individuals)” (Creswell, 2009 p. 476). Collective case study design is when “multiple cases are described and compared to provide insight into an issue” (Creswell,
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2009, p. 477). In this study, multiple cases of online mentoring between a university supervisor and a mathematics student teacher were analyzed for content related to standards-based instruction. Content related to standards-based instruction was analyzed and compared across cases for emerging themes related to various aspects of standards- based instruction. In addition, based on evidence found in online mentoring
conversations, individual cases of student teachers’ developing conception and
implementation of standards-based instruction was described and documented. Findings from this study provide insights into the potential for mentoring student teachers toward standards-based instruction in an asynchronous online environment.
Site Selection
The Master of Arts in Secondary Education with Initial Certification (MIC) program at the university site chosen for this study is an intensive one calendar-year program of 34 credit hours, which leads to both a master’s degree and initial teacher certification. During the fall semester, MIC students take courses on campus for eight weeks and work in interdisciplinary cohorts in area high schools full time for a six-week apprenticeship. In the spring, MIC students continue course work, engage in student teaching and meet together twice a month for a subject specific student teaching seminar. Secondary and middle school mathematics teacher candidates enrolled in the MIC
program have earned a bachelor’s degree in mathematics, mathematics education or a mathematics related field such as engineering or physics. The university supervisors for the MIC mathematics student teachers are former secondary mathematics teachers who have a vast array of experiences in teacher professional development. University supervisors are required to observe student teachers on four occasions throughout the
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student teaching semester and provide feedback during post-lesson discussions, complete written evaluations for each observation and provide a midterm and final evaluation.
Study Participants
Five secondary mathematics student teachers enrolled in a Masters with Initial Certification (MIC) program at a large University in the southeast, United States were selected to participate in this study during their student teaching semester. Study
participants were selected based on the following criteria: The student teacher exhibited the ability and willingness to reflect on his or her teaching practice; The student teaching setting supported the student teacher’s implementation of standards-based teaching practice; The student teacher was willing to participate in the study.
Researcher’s Role and Background
The researcher for this study is a former high school mathematics teacher, who has been involved in the professional development of pre-service and in-service elementary, middle and secondary mathematics teachers for over 20 years. She has worked with elementary and middle school teachers in their classrooms to implement standards-based mathematics curriculum, taught mathematics content courses for pre- service teachers and has served as a university supervisor and mentor for secondary mathematics student teachers. For the past 4 years, she has actively mentored MIC secondary mathematics student teachers online.
In this study, the researcher served as the university supervisor for the study participants. As the university supervisor, she observed each study participant teach a lesson on three occasions throughout his or her student teaching semester, provided feedback during post-lesson discussions, completed written evaluations for each
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observation and completed a midterm and final evaluation. As the researcher for this study, prior to student teaching, she interviewed study participants about their conception of and goals for standards-based teaching. Throughout their student teaching semester, the researcher used the venue of online social networking to consistently communicate with study participants about their student teaching experiences and attend to
opportunities to mentor study participants toward standards-based instruction.
Study Design
Mathematics pre-service teachers enrolled in the Master of Arts in Secondary Education with Initial Certification (MIC) program at a large research university in the southeast of United States were required to keep an online journal of their experiences during their student teaching semester. The MIC mathematics student teachers used the blogging tool within an online social networking site called Ning (www.ning.com) to share their reflections on their classroom experiences with their fellow student teachers and with their university supervisors and mathematics methods instructor. The Ning site was selected because its structure resembles the popular Facebook website where participants can personalize and update their own page. Access to the Ning site was limited to MIC student teachers, their university supervisors and the methods instructors. Student teachers were required to post blogs within their own Ning page three or four times a week that described their student teaching experiences and their personal reflections on those experiences. Research reveals that pre-service teachers’ online communications about their student teaching experiences often lack depth of content and reflection without prompts and feedback from teacher educators (Hsu, 2004; Liang, Ebenezer, & Yost, 2010; Pena &Almaguer 2007). Therefore, the MIC secondary
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mathematics student teachers were provided with the following initial instructions and guidelines to direct their blog postings about their student teaching experiences:
You must post journal entries about your student teaching experiences three to four times a week (minimum). Your journal blog posts should include 1) a description of your student teaching experiences, 2) your personal reflection and reaction to those experiences, 3) your observations about students’ mathematical thinking and learning, and 4) a discussion of the impact of those experiences on your plans for teaching future lessons and your teaching philosophy or knowledge of teaching. Journals should help you formulate and refine your philosophy of education. In order to keep up with the increasing technology demands of our society, we will be utilizing a blog setting for journals at the NING website. All journal entries will be kept confidential (between university supervisors, methods instructor and student teachers) unless permission is granted by the student teacher. Your supervisor will read and comment on your journal/blog posts. In order to create conversation, you are required to comment back to your university supervisor. In addition, you must comment on at least one other post each week. We will be using the blogging to create a dialogue about the student teaching experience, to help you learn, as well as, to encourage and support you in this very important and exciting adventure. In addition, ongoing feedback from university supervisors and methods instructors encouraged student teachers to elaborate and expand their blog posts. The university supervisor read and responded to the study participants’ blog posts throughout their student teaching semester and particularly attended to opportunities to mentor secondary mathematics student teachers toward standards-based instruction via the NING site. Study participants were interviewed prior to student teaching about their conception of and goals for standards-based teaching practices (See Appendix A). At the conclusion of student teaching, study participants were interviewed about their perception of their development toward standards-based teaching. Furthermore, during the post interview, study participants were asked to recall their interpretation of and reaction to specific online mentoring conversations related to standards-based
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instruction (See Appendix B). To help ensure study participants’ honest responses, the post interviews were not conducted by the university supervisor/researcher. Finally throughout the study, the university supervisor/researcher maintained field notes about the study participants’ developing conception and implementation of standards-based teaching practices. The field notes included the researcher’s notes and reflections about face-to-face interactions with study participants (e.g. teaching observations and post observation discussions), as well as her notes and reflections about on-going online communications with study participants.
Data Sources
Audio tape of study participants’ interviews prior to student teaching. The pre- interview provided baseline information about study participants’ conceptions of Standards-based instruction as well as the study participants’ goal for
implementing standards-based instruction
Audio tape of study participants’ interviews at the conclusion of student teaching. The post-interview data provided information about the study participants’
perception of how online mentoring conversation were related to their development of standards-based instructional practices.
University supervisor’s field notes about study participants’ developing conception and implementation of standards-based teaching practices. The university supervisor’s field notes, recorded researcher observations and
reflections about her interactions with student teachers online and during face-to- face post- observations conferences. In addition, field notes were a venue for the
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researcher to process and interpret student teachers developing conception of standards-based teaching practices as it happens– in the moment.
Study participants’ blog posts about their student teaching experiences
University supervisor/researcher’s online responses to study participants’ blog posts
Study participants’ online responses to university supervisor/researcher’s blog posts and responses.
Data Analysis
Qualitative analysis procedures were used to investigate the data in this study. According to Creswell (2009) qualitative analysis involves “examining data in detail to form an in-depth understanding of a central phenomenon through description and thematic development” (p. 254). Thus, this methodology was selected for this study, as the goal for this study was to better understand the phenomena of online mentoring of secondary mathematics teachers. Study participants’ blog post and interview data were reviewed and analyzed for emerging themes in relation to various aspects of standards- based instruction. The results of data analysis were used to form answers to the research questions for this study. The data analysis procedures for each research questions are discussed below.
Data analysis procedure for research question 1
1) What is the contentof mentoring secondary mathematics student teachers for standards-based instruction in an online environment?
a) What is the content of mentoring in an online environment in relation to the following aspects of standards-based instruction:
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elevating conceptual understanding and surfacing ‘big’ mathematical ideas
eliciting and attending to students’ mathematical thinking,
connecting mathematics to real-life contexts,
using and connecting a variety of representations,
facilitating active discovery and mathematical investigations, and
promoting student collaboration and mathematical discourse,
b) What mentoring processes emerge when mentoring secondary student teachers toward standards-based instruction in an online environment?
The researcher analyzed study participants’ and university supervisor/researcher’s blog posts and responses for content related to the aspects of standards-based instruction above. The researcher sorted content from the blog posts into categories aligned with the aspects of standards’ based instruction above. The researcher analyzed the blog posts’ content under each aspect of standards-based instruction for subcategories and emerging themes. The researcher analyzed the university supervisor’s online comments for
mentoring moves that emerged in the online format.
Data analysis procedures for research question 2
2) How are online comments and mentoring conversations related to mathematics student teachers’ developing conception of standards-based teaching practices? (Online
mentoring conversations are defined as segments of online communications that include at the minimum, a student teacher’s initial blog post and a response from the university
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supervisor. In addition, mentoring conversations could include follow-up responses from the student teachers or the university supervisor.)
a) What do student teachers’ online comments reveal about mathematics student teachers developing conception and implementation of standard-based practices? b) How are mathematics student teachers’ self-reported conception and
implementation of standards-based instructional practices related to online mentoring conversations about standards-based teaching?
The researcher reviewed the pre-interview audio data of each study participant to gather baseline information about each participants’ conception of standards-based instruction and goals for implementing standards-based instruction during his or her student teaching internship (See Appendix A). The researcher reviewed the content of online mentoring conversations across the semester for individual study participants. The researcher tracked and interpreted study participants’ developing conception and
implementation of standards-based teaching practices as evidenced in the online comments and mentoring conversations. During post interviews, each study participant was asked to recall and reflect on his or her reaction to specific online mentoring conversations that were related to aspects of standards-based instruction (See Appendix B). The researcher reviewed the audio-tapes of pre- and post-interviews to validate and inform the researcher’s interpretation of individual study participant’s developing conception of standards-based teaching practices as evidenced in online mentoring conversations. Furthermore, the researcher-university supervisor reviewed her field notes for data that might inform her interpretation of online mentoring conversations.
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Internal Validity
Internal validity deals with how closely research findings match reality (Merriam, 1998). In this study, internal validity will be addressed through member checks,
triangulation and clarification of researcher bias.
In qualitative research, the interpretation of reality is mediated through the researcher (Merriam, 1998). For this study, the validity of the researcher’s interpretation of the reality of online mentoring conversations was enhanced by member checks. During post interviews, study participants were asked to recall their interpretation and reaction to specific online mentoring conversations related to standards-based instruction (See Appendix B). To help ensure study participants’ responses do not simply reflect what the university supervisor wanted to hear, the post interviews were not conducted by the