Supporting teacher professional development through online video case study discussions: An assemblage of preservice and inservice teachers and the case teacher

Teaching and Teacher Education 25 (2009) 1158–1168

Contents lists available at ScienceDirect

Teaching and Teacher Education journal homepage: www.elsevier.com/locate/tate

Supporting teacher professional development through online video case study discussions: An assemblage of preservice and inservice teachers and the case teacher Yusuf Koc a, *, Deniz Peker b, Aslihan Osmanoglu c a b c

IUN School of Education, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA Department of Biochemistry, Virginia Tech, Blacksburg, VA 24061, USA Trakya University, Edirne, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 August 2007 Received in revised form 29 December 2008 Accepted 24 February 2009

The purpose of this study was to explore the potential value of online video case discussions among preservice and inservice teachers, and the video case teacher as a tool for the professional development of teachers. Participants included a total of 26 preservice and inservice mathematics teachers and a veteran teacher who appeared on the video case. Using content analysis techniques, we provided a thematic analysis of the teacher discourse and demonstrated the exchanges between the participating teachers and video case teacher. We also assessed the overall effectiveness of our online forum set up for the professional development of teachers. Results indicated that participant teachers were able to make theory–practice connections by articulating specific frameworks that guided our study. The inclusion of the video case teacher was beneficial for the other teachers in several ways. We contend that online forum discussions of video cases in which collective engagement of preservice and inservice teachers, and the case teacher have a great potential to support teacher professional development. Ó 2009 Elsevier Ltd. All rights reserved.

Keywords: Case-based instruction Case discussions Preservice teacher education Inservice teacher education

In this study, we created a community of preservice and inservice teachers within the context of three different mathematics teaching methods courses at a regional campus of a large researchintensive university in the United States. We brought preservice and inservice teachers together for the purpose of connecting theory with practice by fostering discussion, reflection, and the sharing of thoughts on teaching and learning through an online video case. The video case teacher was also a participant in the discussions. Discussions regarding the video case took place in an online forum hosted by the university’s main campus. Our purpose was to explore to what degree the case discussions generated opportunities for the participants to build a connection between theory and practice. 1. The use of cases in teacher education Cases have been used for different purposes in teacher education at least for over two decades. They have been used to develop critical thinking skills (Mayo, 2004), improve and increase

* Corresponding author. Tel.: þ1 219 980 6592. E-mail addresses: [email protected] (Y. Koc), [email protected] (D. Peker), [email protected] (A. Osmanoglu). 0742-051X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tate.2009.02.020

reasoning (Lundeberg, 1999) and facilitate decision-making skills (Jay, 2004; Merseth, 1992). Cases have also been used in subject specific contexts to develop pedagogical and professional knowledge (Manouchehri, 2002; Mayo, 2002), extend metacognitive skills (Lundeberg, 1999), and bridge the gap between theory and practice (Bencze, Hewitt, & Pedretti, 2001; Masingila & Doerr, 2002; Schrader et al., 2003). Lundeberg, Levin, and Harrington (1999) contended that use of cases in teacher education provide opportunities for teachers to apply their theoretical and practical knowledge to classroom contexts. According to Bencze et al. (2001), this is important because the ‘‘apparent chasm between what often happens in university-based teacher education and teaching in schools – a theory–practice gap – has caused some jurisdictions to shift much of their teacher training efforts out of academia and into the field’’ (p. 192). As Bencze et al. noted, cases have the potential to reduce theory–practice gap. Cases are useful tools as they reflect the characteristics of a real classroom and provide a context for preservice teachers to prepare for realities of teaching (Butler, Lee, & Tippins, 2006; Masingila & Doerr, 2002). By analyzing cases, teachers get an opportunity to understand what could happen in a classroom given a specific scenario (Lundeberg & Levin, 2003; Lundeberg et al., 1999). They also gain perspectives on teaching in settings different from their field experience sites or their own classrooms (Merseth, 1992).

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

2. The use of video cases in teacher education There is an increasing interest for integrating information technologies into the use of cases in teacher education (Boling, 2007). Video cases are useful tools for teacher education for several reasons; unlike written cases, video cases allow teachers to see the complexity and richness of a real classroom setting by capturing voices, body language, interactions, and more realistic picture of the learning environment. Thus, video cases lend themselves to potentially richer discussions of teacher practices and help teachers connect theory and practice better (Brophy, 2004; Seago, 2004). Masingila and Doerr (2002) reported that multi-media cases support preservice teachers’ understanding of the complexity of teaching, guide their instructional practices and help connect their own practice with that of the teacher in the video case. Similarly, Sherin and van Es (2005) documented that as a result of watching video cases, overtime, both preservice and inservice teachers showed gains in their ability to discern and interpret the features of classroom teaching. Previous research also indicated the overall benefit of interactive video case discussions for improving the quality of teacher discourse and reflection (McGraw, Lynch-Davis, Koc, Kapusuz-Budak, & Brown, 2007). Despite the promising findings reported above, research on the effectiveness of video and multi-media cases in teacher education is still in its infancy (Boling, 2007; Lampert & Ball, 1998; Masingila & Doerr, 2002). One aim of this study is to examine the effectiveness of video case discussions in promoting the quality of teacher reflection and discourse in general. Although discourse analysis is a broad field and there are plenty of approaches to analyze speech and text (Titscher, Meyer, Wodak, & Vetter, 2000), specific techniques and strategies available to measure the quality of discourse is scarce. By quality, we refer to the depth and richness of the topics discussed. We are not aware of any research that particularly focuses on the quality of teacher discourse in online environments or specific techniques available to measure discourse quality. There is, however, some research that focuses on the effectiveness of online forum environments. Guzdial and Turns (2000) suggest two basic criteria for online forums to be effective: (1) sustainability and (2) discussions focusing on the learning goals of the course. Sustainability refers to the development of message threads through responses to an initial message; the number of messages written in response to a particular message contributes to the sustainability of the forum discussions. The other criterion is related to whether contributions to the forum are on-topic or offtopic. We employed these two criteria in our analysis of the effectiveness of the forum discussions.

1159

together in the same learning environments to discuss various aspects of teaching and learning through video cases (Arellano et al., 2001; McGraw et al., 2007), the number of studies of this type is limited and further research is needed in this area. Another significance of our study is the utilization of an online forum for case discussions. This online tool offered participants opportunities to analyze the practices in a mathematics classroom with all its complexities in an asynchronous mode. Our literature review indicates that only a few studies with similar components have been conducted (McGraw et al., 2007; Nemirovsky & Galvis, 2004). 4. Research questions Our research questions are: (1) To what degree are teachers able to make theory–practice connections in response to a video case of mathematics instruction? (2) What dimensions of teaching are discussed in response to a video case of mathematics instruction? (3) To what degree online forum discussions are effective tools when preservice and inservice teachers as well as the video case teacher participate in the discussion; and what is the potential value of such an arrangement in case-based pedagogy? 5. Methods 5.1. Setting The data were collected in the context of three different mathematics methods courses in a 4-year college that is part of a large university system in the Midwestern United States. The first author was the instructor of all three courses. Two of the methods courses were designed for preservice teachers – one for elementary education majors and one for secondary mathematics education majors – and the third course was a graduate level mathematics teaching methods course designed for experienced teachers enrolled in a Master’s program in elementary or secondary education. Both undergraduate courses were intended to provide preservice teachers with a broad understanding of how school mathematics is structured and learned. The graduate course was intended to help inservice teachers improve the teaching of mathematics in elementary and secondary classrooms. As a course assignment, all students were required to view and reflect on a video case of mathematics instruction available on an online forum. 5.2. Video case

3. Significance of the study We believe this study contributes to the literature in three distinct ways. First, our research design is unique in that it includes the participation of the video case teacher in the discussions. The preservice and inservice teachers in this study had the opportunity to understand the case teacher’s motivations and plans for her teaching practices depicted in the video. The inclusion of the video case teacher also enabled participants to check the validity of their interpretation of the video case. This occurred as the teacher in the video responded to criticisms, comments and questions raised by the participants. We believe this set up has the potential to increase the quality of the case discussions and reflections. Because the effectiveness of online forum environments is still under question, this study sheds light on the potential value of online forum discussions in teacher education. Even though previously researchers brought preservice and inservice teachers

The video case, Revisiting Doubles, represented third grade mathematics instruction and it was 57-min long. It was produced as part of a large online teacher development project with the goal of building online teacher learning communities, and only members of the forum had access to the video. The authors were not involved in the making of the case. The topic of the video lesson was doubling (multiplication by two). At the beginning of the lesson, Melissa, the video case teacher, taught the concept of doubling while revisiting the work students had done on doubles and halves from an algebraic perspective. She focused on the topic using a story, ‘‘Two of Everything’’ (Hong, 1993), to get students’ attention. After reading and talking about the story in the book, she used a T-chart to teach the doubling concept in connection with the story. The students used the T-chart to look for patterns in the numbers, and they wrote algebraic equations. Following the T-chart activity, students worked on their math projects.

1160

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

5.3. Existence of multiple roles With respect to the roles taken, the forum environment included (1) the course instructor who was the moderator of the forum, (2) Melissa whose teaching was scrutinized by all students and (3) the students who contributed to the forum as part of their course requirements. We distinguished these roles with the following identifiers: ‘‘the moderator’’, ‘‘the critiqued’’ and ‘‘the critiquers.’’ ‘‘The moderator’’ was the instructor, ‘‘the critiqued’’ was Melissa, and ‘‘the critiquers’’ were all students in the forum. In all cases, Melissa was the responding person; she never initiated a topic of discussion. A detailed analysis of Melissa’s contribution, and how the roles of ‘‘critiquer’’ and ‘‘critiqued’’ played out are provided in the results section. 5.4. Role of the instructor The instructor designed all course assignments to promote the teaching of mathematics for student understanding. The theoretical background of the course assignments and classroom discussions were instituted by the integration of Making Sense: Teaching and Learning Mathematics with Understanding (Hiebert et al., 1997), a book that emphasizes teaching mathematics with understanding. At the beginning of the semester, the students in the three methods courses read and engaged in whole class discussions regarding Making Sense during regular class meetings. In order to put theory into practice, the instructor designed the online video case discussions that are the focus of this study. 5.5. Melissa, the video case teacher Melissa had been teaching elementary students for over 20 years. She was teaching third graders in an elementary school of a middle-class neighbourhood in a college town in the United States. She was also teaching mathematics methods courses at a local university as a part-time instructor. Prior to the start of the semester, the instructor invited Melissa to join the online discussions regarding her video case, Revisiting Doubles. She agreed and actively participated in the online discussions. The students did not know Melissa in person and neither Melissa’s comments on the forum nor the students’ comments on Melissa’s teaching affected students’ grade. 5.6. Student participants Twenty-six students participated in this study. Nineteen of the participants were undergraduate students and seven were master’s students. Among the 19 undergraduates, 13 were juniors taking the elementary mathematics teaching methods course and had one semester left before student teaching. The remaining six undergraduates were enrolled in the secondary mathematics teaching methods course and were seniors who were planning to student teach the following semester. The master’s students were inservice teachers teaching in elementary and secondary schools. 5.7. Data sources The data consisted of participants’ responses to a video case. While participants had access to a variety of sources (interviews with the teacher, lesson plans, sample student works, and links to outside resources), throughout the discussions, participants commented only on the video and did not refer to those sources. During the three-week long discussions, preservice and inservice teachers responded to the instructor’s discussion prompts (Appendix A), and were free to raise their own discussion topics. They posted 129

messages; in addition, the course instructor and Melissa sent 35 and 28 messages, respectively. These messages, 192 in total, were the focus of the data analysis. Table 1 represents the average number of postings and range of postings per person. We excluded messages that were too short from the analysis, such as ‘‘thanks’’ or ‘‘I agree’’, and the parts of some messages that were irrelevant to our research purpose, e.g., asking the due date of an assignment or making an announcement of an event. 5.8. Data analysis To explore to what degree case discussions created opportunities for the participants to connect their theoretical and practical knowledge, we utilized content analysis techniques (Neuendorf, 2002). ‘‘Content analysis is a research method that uses a set of procedures to make valid inferences from the text’’ (Weber, 1990, p. 9) and it often summarizes interpretations by reporting quantitative measures (Neuendorf, 2002). The unit of analysis was an entire message sent by a participant. De Wever, Schellens, Valcke, and Van Keer (2006) note that the choice of the unit of analysis depends on the context, and researchers have the choice of taking complete messages in a discussion as the unit of analysis. In our study, we examined individual messages in their entirety because most of the time, paragraphs in the messages or even a single paragraph included more than one idea, often intertwined, that matched our codes. It was inextricably difficult to focus on smaller units, such as a sentence. In analyzing individual messages, we asked the question ‘‘What ideas (e.g., student understanding, a specific teacher role) are mentioned by the sender?’’ When more than one idea was expressed in a message, it resulted in multiple coding. In some lengthy messages, we assigned up to five codes. Most messages were coded with more than one code with an average number of 1.9 codes per message. Appendix B demonstrates how we assigned multiple codes to a single message. The codes and their descriptions are represented in Table 2. ‘‘The nature of task,’’ one of Hiebert et al.’s (1997) critical dimensions of mathematics classrooms, was not among the final coding categories because the discussions about ‘‘the nature of task’’ were included in two categories, teacher roles and student understanding. For instance, the teacher as manager category included all the instances where the participants talked about teacher role involving task selection and implementation. In addition, the student understanding category included the discussions on student understanding resulted from their implementation of the task in the case. In general, we formed all coding categories to capture the discourse on mathematics instruction. We did not have separate categories for mathematics and mathematics instruction; the existing categories covered various aspects of mathematics instruction including mathematical understanding. For instance, the category student understanding addresses how students learn the mathematical content in the video case. The second type of analysis we made was about the effectiveness and quality of online forum discussions by using the two criteria we previously mentioned: sustainability and on-topic/off-topic characteristics of messages (Guzdial & Turns, 2000). In the results Table 1 Number of postings by the participants.

Preservice (n ¼ 19) Inservice (n ¼ 7) Case teacher (Melissa) The instructor

Number of postings

Average number of postings per person

Range of posting numbers

96 33 28 35

5.05 4.71 N/A N/A

3–8 3–6 N/A N/A

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168 Table 2 Descriptions and usage of the coding categories. Coding categories  Teacher roles Teacher as manager

1161

communication and reasoning. We coded all discussions about the NCTM standards under one theme, standards.

Descriptions

5.10. Coding reliability B

Teacher as facilitator

B

Teacher as assessor

B

Teacher as instructional decision maker

B

 Student understanding

B

 Standards

B

 Integration

B

 Classroom culture

B

 Equity and accessibility  Tools

B

B

Teacher role involving task selection and implementation, and classroom management (macro level management) Teacher role involving creating a learning environment to promote student understanding and allowing students to be cognitively active Teacher role involving formal and informal assessment of student learning Teacher role involving actions at a given point of ongoing unit of instruction in order to make the instruction more efficient (micro level management) Evidence of student learning and understanding as interpreted by the participants in response to a specific instance in the video case or student learning and understanding in a more general sense (please note; the instances where the participants talk about the teacher’s facilitation of student understanding are excluded) The instances where the instruction is reflected upon with respect to the NCTM and district standards or the standards themselves are discussed The instances where integration of mathematics with other subjects are discussed Cultural aspects of classroom organization, and teacher-student and student-student interactions Equitable access to materials, task, and learning opportunities The instances where the value of using tools (physical, symbolic and discursive tools such as manipulatives, charts, books, symbols) in mathematics instruction and the tools themselves are discussed

We followed several procedures in order to ensure coding reliability. First, we individually coded approximately one-fourth of the data set; then, we compared the coded units to see what percentage of the units matched across the group members. Initially we found a match of approximately 70%. In order to increase this percentage, we narrowed down the codes that caused ambiguity and accounted for the decrease in coding reliability. Meanwhile, we also added some new codes in order to better demarcate teacher roles (e.g., teacher as instructional decision maker). With these new adjustments, our coding reliability reached 80%. Finally, we decided to code the entire data set in a three-way conference by going over every single message. Prior to the conferences, we coded the messages individually and during the conferences, we shared and discussed our coding with each other. When disagreements emerged in labelling a code, the group negotiated the meanings and agreed on a final coding. 6. Results In this section, we provide the results of two types of analysis. First, we present our findings of the content analysis that is about the characteristics of teacher discourse, including the video case teacher’s contribution. Second, we provide an effectiveness and quality analysis of the teacher discourse with regard to use of online forum discussions in teacher education. For clarity, in reporting our findings we use pseudonyms that start with the letter ‘‘P’’ to denote preservice teachers and pseudonyms that start with the letter ‘‘T’’ for inservice teachers. We refer to both preservice and inservice teachers’ discourse together as ‘‘Teacher Discourse’’ in this section. 6.1. Content of teacher discourse

section, we provided some quantitative measures (e.g., number of messages per thread) to address the sustainability criterion and further interpreted teacher discourse to address the issue of quality. 5.9. Coding frameworks In creating our coding framework, we primarily drew upon from the book Making Sense: Teaching and Learning Mathematics with Understanding (Hiebert et al., 1997). The book provides a fivedimensional framework to analyze mathematics classrooms: the nature of classroom tasks, the role of the teacher, the social culture of the classroom, mathematical tools, and equity and accessibility. We initially created a coding schema based on these five dimensions, later we refined our coding in order to represent more details of teacher discourse that were not completely captured by our initial schema. The second theoretical framework was the National Council of Mathematics Teachers (NCTM) standards including problem solving, communication, connection (integration), representation, and reasoning and proof (NCTM, 2000). The standards were selected as a framework because they have great influence on mathematics education, including the curriculum (Senk & Thompson, 2003) in as much as they represent a common philosophy-teaching mathematics for understanding (NCTM, 2000). There is evidence showing that the standards have been successful in improving the quality of classroom teaching (Kilpatrick, Martin, & Schifter, 2003). The standards were coded as a single theme rather than separate components such as problem solving,

We organized this section under five themes. Each of these themes represents the most salient aspects of teacher discourse we identified in our content analysis. 6.1.1. Theme 1: Teacher roles Teacher roles were the most dominant elements of teacher discourse. We identified four distinct teacher roles: teacher as manager, as facilitator, as assessor, and as instructional decision maker. We presented a definition of each of these roles in Table 2 with examples from our data (see Appendix C). The teacher roles overall accounted for 46.5% of all codes used (Fig. 1). Among them, facilitator was the most commonly discussed, followed by manager and instructional decision maker roles. On the other hand, participants talked about assessor role in only a few instances. Drawing from Wells’ (1999) conceptualization of micro and macro levels of teaching, we categorized teaching roles into micro and macro levels. Specifically, the instructional decision maker role represented the micro level and the manager role represented the macro level teaching. Wells defines the micro level as follows: At the micro level.teaching can be characterized much more in terms of response. Having created the setting and provided the challenge, the teacher observes how students take it up, both individually and collectively, and acts to assist them in whatever ways seem most appropriate to enable them to achieve the goals that have been negotiated (p. 243). By micro level, we mean that the role of the teacher is thought to be performed in a relatively short period of instructional time often

1162

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

Teacher as Assessor

4

Equity & Accessibility

Number of messages: 129 Number of assigned codes: 245 Number of codes per message: 1.9

9 20

Integration

Codes

Standards

21

Classroom Culture

22

Tools

29

Teacher as Inst. Decision Maker

29 30

Student Understanding Teacher as Manager

37

Teacher as Facilitator

44 0

5

10

15

20

25

30

35

40

45

50

Frequencies Fig. 1. Frequency distribution of the codes.

in response to an emerging teachable moment or to a need to switch in student tasks. We envision micro roles as more spontaneous acts rather than planned acts, though we believe good performances of micro roles are commensurate with the teaching experience. The following example from Pearl, an elementary preservice teacher, demonstrates how the role of teacher as instructional decision maker plays out: After viewing the second segment, I personally do not think she [Melissa] steered them in the right direction. She didn’t really reinforce what they had just picked up. I think I would have discussed the book, then allowed the students to work with manipulatives to continue to discover the pattern of doubling, which would have lead to a better discussion and communication by the students. Pearl identified several actions that Melissa did not perform. Pearl describes this situation as ‘‘not steering the student in the right direction.’’ These types of micro level decisions require teachers to react instantly to students’ responses as the instruction unfolds itself. The other level of teaching is the macro level. Wells (1999) put it as follows At the macro level, the teacher is the chief initiator and is responsible, among other things, for selecting the themes for curricular units and the activities through which they are to be addressed. These decisions should be based on both knowledge of students’ interests and current level of participation and on expectations concerning the semiotic resources that such themes and activities are likely to call into play (p. 243). In our conceptualization, the teacher as manager role, which is a macro level teaching, is mostly planned and executed in broader periods of time frames, including out-of-class periods. The macro level manager role consists of teacher acts that are associated with establishing the norms of class order, determining codes of student behaviour, and other broad level of planning. For instance, the following quote from Priscilla, an elementary preservice teacher in the study, represents how the manager role and classroom culture are interwoven together: I really like how Melissa uses work stations in her classroom! The students are given freedom to learn in a way that is best for them. She also makes them responsible for themselves by

having them clean up their messes and control themselves while at the stations. I have only seen this in a few classrooms, and in those classes the students rarely experienced that so the scene was chaotic. Here though she shows that if it is used often, students will behave and work hard at stations. Priscilla saw that Melissa’s control over the classroom is a successful example of classroom management without diminishing student freedom. Another distinct teacher role is that of a facilitator. A good facilitator not only provides a physical environment for learning but also provides affective and moral support for students (Bonk, Wisher, & Lee, 2003). Polly’s, an elementary preservice teacher, observations are of this kind: I also agree with Paprika, I noticed how Melissa really encourages her students not to just know something but to be able to also explain it. I believe this to be very important! It is really easy to memorize, but not as easy to learn. If teachers encourage their students to explain and show reasoning of their answers, it makes them think through the ways that they go about conquering a problem. A student cannot just say that ‘‘yes’’ they know how, but they have to show that they know how!

6.1.2. Theme 2: Student understanding The second most common part of the teacher discourse was student understanding. It was not surprising to see student understanding among the most discussed topics since there was a direct relationship between some teacher roles and student understanding. The facilitator and instructional decision maker roles are directly related to improving student learning and understanding. In the following quote, Ted, an inservice elementary school teacher, criticizes the teacher’s performance and provides an example of how student understanding is closely linked to facilitator role: I believe the desire to share student thought is present, but not effective. Children need to be able to think about what is being presented and have the opportunity to challenge the information based on what they know, understand, or perceive based on their prior experiences. By allowing and encouraging cognitive conflict you are empowering children with the ability to

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

critically think and take a concept, dissect it, and analyze its validity and truth. Similarly, a secondary preservice teacher, Patrick, observes the link between student understanding and facilitator role of the teacher as follows: Students that make math problems their own, generally analyze process, solve, and retain that problem better than students that do not take ownership of the problem. The process of ownership of the problem allows students to explore and personalize the information being presented in the class. All of this promotes communication and reflection which are necessary components for owning the information that was learning. The role of the teacher is attempting to engage students to take ownership of a problem. In the video, this was attempted through group work and the use of manipulatives. Although there was an attempt to accomplish this, it isn’t a guarantee it will happen. When discussing the participants mentioned several different indicators of student understanding. Among those are ownership of the problem (as noted above), transferring knowledge to a new situation, communicating the findings efficiently, being able to visualize or imagine the undertaken problem and demonstrate it through manipulatives, and facial expressions and some other body language during a participatory activity. Overall, this variety of evidence for student understanding suggests that our participants captured the multifaceted dimensions of student understanding. 6.1.3. Theme 3: Use of tools and integrating other subjects in teaching A large majority of the teachers appreciated using tools and integrating other subjects into mathematics teaching. In the video case, Melissa uses a story, ‘‘Two of Everything’’ (Hong, 1993) to tap into her third graders’ prior mathematical knowledge. Most participants thought that integrating literature into mathematics was a ‘‘great idea’’, and they believed that different kinds of tools (stories, manipulatives, charts, etc.) supported mathematics learning. For instance, Phil, a secondary preservice teacher, thought that starting the lesson with a story was an excellent way to get student attention: Using the story as an ‘‘opener’’ for the lesson was an excellent way to get the students motivated and excited. The importance of reading, especially at that age was a good connection with another subject. An elementary inservice teacher, Trisha, described the value of tools in the following words: There were many manipulatives in this classroom and they were used pretty effectively. I love to use the T-chart in my classroom also – with manipulatives and just as mental math. I agree with Ted that the jump from doubling to tripling may have been a little too fast unless the students had worked on this previously. It was interesting to watch the children have the manipulatives and the journal on the desk together so that they could go right from one to the other. At second grade it’s a good idea to go from concrete to abstract quickly. As Trisha observed, manipulatives can be used to ease the transition process from concrete representation of mathematical ideas to abstract level of mathematical thinking through symbol systems. 6.1.4. Theme 4: Classroom culture and equity and accessibility Classroom culture, and equity and accessibility issues were the two topics that were discussed hand in hand. Contemporary views

1163

on student learning (Hiebert et al., 1997; NCTM, 2000) emphasize establishment of learning communities wherein all learners are provided with equitable access to materials and are encouraged to participate in discussions. Our analyses showed that participants were well observant of issues related to classroom culture and equity. Tess, a secondary inservice teacher, highlights the role of classroom teacher in providing learning opportunities for every child in class: I think your [to a preservice teacher] observation was very important. Many children are not given the opportunities to acquire knowledge in the classroom in a manner which is meaningful to the student. Melissa made every effort to create an environment that provided an opportunity for all students to openly participate in this lesson on a level that was interesting and meaningful for that student. Two most commonly articulated aspects of classroom culture were children’s freedom to move around in the classroom, and their ability to share their products with other students in the class, thus increasing mathematical communication. Tara, an elementary inservice teacher, describes her observations of the classroom culture as follows: The work centres allow Melissa to promote a positive social culture in her classroom. Students can choose and share their activities with their classmates as they move around the classroom and address each centre. The interaction between the groups encourages students to learn from each other, as well as discovering concepts on their own. Another important concept noted by participants was accessibility. Trisha, an inservice teacher, observed that accessibility is a term that applied to both the task and the teacher: Perhaps it is just as important for the teacher to be accessible as it is for the task to be accessible. I think Melissa did a good job of taking something positive from each student’s thoughts or hypothesis. Students were given an opportunity to be heard. But tasks themselves are not always accessible to every student. In that case instruction is very important and the teacher must be accessible to guide and encourage student learning. 6.1.5. Theme 5: NCTM standards As a part of the online discussions, the instructor prompted the participants to examine the extent to which the video case reflected an implementation of the NCTM standards. Although the standards do not have a high frequency in Fig. 1, the impact of the NCTM standards on the video case discussions was much larger. Perhaps this is because our coding schema reflected the most salient aspects of teacher discourse, while a tacit representation of the standards remained in the background of the discussions. For example, we coded the following message primarily as student understanding because the crux of this message is about student understanding. However, one can realize in the same quote how the indicators of standards help assessing student performance: The children were actively engaged in problem solving. They were asked to explain their reasoning for their answers. When the students were at their desks working, a young lady found a pattern. The teacher asked her to communicate her findings to the whole class. The fact that she could communicate it effectively means that she understood what was being taught (Palmira). Palmira, an elementary preservice teacher, observed standards such as problem solving, reasoning, and communication as process skills in deciding student understanding. Examples of this sort were

1164

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

frequent throughout the discussions. The standards Palmira noted refer to student understanding in both literature (Hiebert et al., 1997) and NCTM standards (NCTM, 2000). Another example for how standards are discussed by teachers is provided in Appendix C. 6.1.6. Melissa’s contribution to the discussions Melissa, the case teacher, posted a total of 28 messages to the discussion forum. In analyzing these messages, we juxtaposed each message of Melissa with the corresponding student message. By looking at the branching of message threads, we were able to pinpoint to whom Melissa responded. In our analysis, we tried to identify Melissa’s intentions for writing each message. We identified the seven coding categories presented in Table 3. In Table 4, we present the corresponding sample quotes and codes. As demonstrated in Table 4, most of the time we assigned more than one code to an individual message because multiple intentions co-existed in the same message. As seen in Table 3, Melissa’s most common response characteristic was confirmative in nature, that is she approved a comment or idea expressed by students. For instance, in response to Panna’s message addressing how Melissa’s use of different tools and manipulatives provide a different way of learning, Melissa said, ‘‘every time you do any type of activities, you are providing an opportunity for the students to make connections and thus another way to remember.’’ Here Melissa confirms Panna’s idea of ‘‘providing a different way of learning’’. The second common characteristic we observed was Melissa’s explanatory responses. Being critiqued by preservice and inservice teachers, Melissa naturally provided explanations for why she acted in certain ways. Student critiques were mostly centred on her ‘‘classroom management’’ and ‘‘instructional decision making.’’ The following pair of quotes illustrate how the roles of critiquer and critiqued were enacted: .I do not believe that Melissa met the NCTM standards completely. It’s like she skimmed the water, but did not go deep enough. I see what you see when you stated that she did not have the students grasp the concept. I do think that she started the lesson good by reading a story. It seems that she had the students engaged because she made the task meaningful to them. But like I stated earlier in my replies, it seems like ‘‘show and tell’’. Students should not just reply an answer; they should communicate and reflect (Penelope, an elementary preservice teacher) Melissa responded to this message as follows: When you are learning something new, how deeply can you go when you first introduced to the topic? Understanding is built by layers! As seen in the last sentence of the above quote, Melissa often made aphoristic statements about mathematics teaching. We Table 3 The distribution and description of codes with regard to Melissa’s contribution. Codes

Number of messages

Descriptions

Confirmative Explanatory

14 9

Appreciative Informative

8 7

Aphoristic Self-inquisitive

6 3

Suggestive

2

Approving an idea or comment. Providing an explanation for the reasons why she acted in a certain way. Appraising or thanking for a positive comment. Providing extra information and/or insight which are not readily observed in the video case. Expressing insightful, wise and short sentences. Wondering and reflecting about her own teaching practice. Advising ideas or recommending resources for the students.

Table 4 Coding of Melissa’s contribution and sample quotes. Codes

Sample quotes

Confirmative Appreciative Explanatory Informative

‘‘You are so right about the facial expressions and physical movements. Very observant!’’ ‘‘The lesson you observed went from 12:50 until 2:45. These children are 8 and 9 years old. It is impossible to do the same thing for that amount of time. The content standards I was attempting to address were number and operations (place value and multiplication) and some algebra. ‘‘Mathematicians are pattern seekers!’’ [By confirming the corresponding remarks]. ‘‘I agree. Just because a book hits a topic you are teaching, it is not necessarily a good book. Be choosy and DO remember your reading method classes.’’ ‘‘Usually I try to ask what others think.I’ll have to go back and view that part again. I may have kept on going because I sensed that the kids had had enough for that moment. I think you make a good point.’’

Aphoristic Confirmative Confirmative Suggestive Explanatory Self-inquisitive Appreciative

operationalize aphorisms as short, witty, insightful stand-alone sentences that often express a view of experience (Morson, 2003). Melissa typically used aphoristic statements to either confirm or refuse an idea. Some other examples of aphoristic statements made by Melissa are ‘‘Mathematicians are pattern seekers!’’; ‘‘Surround the child with the concept’’; ‘‘Some children just get it, and others get it when they see it’’; and ‘‘Learning math is a multi-layered endeavour.’’ We hypothesize that by using aphoristic statements Melissa was able to say more in fewer words. Another feature we observed in Melissa’s messages was providing extra information not readily observed in the video case. This usually happened when Melissa was making explanations. While she was justifying her acts, she also enlightened the students with ‘‘behind the scene’’ information which was otherwise unavailable. For example, when criticized for not aligning her instruction with the standards, Melissa responded: We worked on these number stations on place value over a period of two months. The conversation about subtraction has been continuing on and off for the entire year. It is impossible to teach mastery in one day. I wasn’t trying to do that. By revealing that the ‘‘place value’’ topic had been going on for two months, and that subtraction had been a continuing topic, she tried to help teachers understand that mastery is not achievable in a short period of time. The other codes we assigned to Melissa’s messages included appreciative, self-inquisitive and suggestive characteristics. Appreciative messages required the least interpretation since most of them were straightforward. Most of these messages contained phrases such as ‘‘thank you’’, ‘‘I appreciate,’’ etc. The messages in which Melissa questions and reflects on her own practice (categorized as self-inquisitive) were scarce. One example of this is when Melissa responded to Ted’s message in which he stated that he was unable to see the whole picture with so many things happening in the classroom, and that he did not have an idea about how students would be assessed. In response to this, Melissa said If I am assessing for a grade, I collect lots of evidence. Work samples, tests, individual interviews, strategies I see them using and that they can communicate with me. I know it looks chaotic, but you saw just one part of a whole. Melissa here reflects on her teaching and admits that her class looks chaotic. Lastly, Melissa also made suggestions for the participants; an example of this appears at the bottom of Table 4.

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

1165

6.1.7. Instructor’s contribution to the discussions Besides his role in the overall organization of the course, the instructor moderated the forum by monitoring the students’ progress and encouraging them to participate in the discussions. More specifically, the moderator role was enacted through several action categories: initiating a discussion, giving positive feedback, asking for clarification, asking for elaboration, questioning, revoicing or rephrasing, asking for concrete examples of the ideas, and sending notes to the attention of the students. The instructor posted 35 messages each of which fits into one of the aforementioned categories. Some examples of instructor prompts are provided in Appendix A.

how teachers make theory–practice connections. We also assessed the effectiveness and quality of online forum discussions as a learning tool for teacher education. Our study was unique and innovative in that it included components that do not so often come together in the same research study: preservice and inservice teachers, case teacher, use of video case and online forum discussions. We allocate this section for a discussion of our results and the effectiveness of video cases and the inclusion of case teacher in the discussions.

6.2. Effectiveness and quality of case discussions

In our literature review, we mentioned many uses of cases in teacher education. Our purpose of using cases in this study was to promote theory–practice connections through discussions and reflections. Our results suggest that online forum discussions about the video case is a productive tool that helps teachers to make stronger theory–practice connections. We documented evidence showing how teachers capture various aspects of mathematics instruction in a video case. Teachers articulated ideas from two theoretical repositories: Making Sense and NCTM standards. Teachers were able to connect what they read and study in their methods course with what they critically watch in the video case. As shown in the results section, we found four different teacher roles discussed at two different levels (i.e., micro and macro). Teachers were also able to identify other facets of mathematics instruction such as student understanding, equity and accessibility, the standards, etc. (Fig. 1). The following quote from Polly, a preservice teacher, documents how teachers used the language and philosophy of Making Sense and the standards to reflect on the video case:

Earlier we introduced two criteria to judge the effectiveness of forum discussions, sustainability and focusing on the learning goals of the course. Based on these criteria, we analyzed the effectiveness of the forum discussions. Previous research with undergraduate students indicates that the average number of messages in online forum discussion threads is less than two (Whittaker, Terveen, Hill, & Chemrny, 1998). Guzdial and Turns (2000) reported an average of 4.2 messages when they utilized a specific online forum tool designed to promote online discussions. In our study, the participants initiated 31 threads in total. The range of messages varied from one to 17 in the threads. Within these threads, the students posted 129 messages and Melissa posted 28 messages. Thus, the average number of messages per thread including Melissa’s posts was 5.16 in our study, higher than in previous studies. With respect to the criterion regarding whether the discussions focused on the learning goals, we can say that all the messages posted by students were related to the video case in accordance with the instructor’s directions. In addition to the effectiveness measures described above, we suggest two other criteria that might be indicators of quality of teacher discourse. The first one is the interconnectedness of the discussed topics. Our content analysis showed that, rather than focusing on single isolated ideas, participants generally discussed more than one idea at a time. For example, communication one of the standards was discussed together with classroom culture or teacher as facilitator was discussed with student understanding. The average number of codes assigned for each message was almost two (1.9), meaning that participants discussed about two topics in each message. We interpret this figure as an indicator of quality with regard to ‘‘richness.’’ The second criterion that we envisioned is the existence of multiple levels (i.e., micro and macro levels, Wells, 1999) in the discussion of teacher roles, which refers to the quality with regard to ‘‘depth.’’ Even though this criterion applies only to the teacher roles, one should notice that teacher roles overall account for approximately half of all assigned codes (46.5%) (Fig. 1). Previously, we made the distinction between these two levels of teacher roles. By thinking about teacher roles in two different layers, respondents gave depth to the discussions. They were also able to zoom in and out to the teaching roles, which we believe can account for a quality measure. In summary, the online forum environment in our research was deemed effective by the standards set by current research literature. In addition, our data presented evidence for quality in terms of both ‘‘richness’’ and ‘‘depth’’.

7.1. Theory into practice: revisiting the purpose of using case discussions

I noticed that the way that Melissa teaches, she implements many of the standards. The two that really seemed to stand out to me were communication and problem solving. Melissa really promotes a lot of problem solving in her classroom. Even if the students are having trouble coming up with the correct answer, she really tries to push them into figuring out a method of reasoning on their own. She never gives the students the answer that she is looking for, but tries to give them clues in the direction that she wants them to go. She also encourages communication in her classroom, which I believe to be a key element in a math class. Students need to be able to discuss with one another about the ways that they go about figuring things out. Polly refers to two NCTM standards, communication and problem solving, and connects the problem solving standard to major ideas introduced in Making Sense. In particular, she points out that Melissa did not give the correct answer to students but guided their thinking to her goals. Polly also reports that Melissa only provided the necessary clues thereby encouraging communication among her third graders. These statements are close to the ideas espoused in Making Sense. Hiebert et al. (1997) strongly support the idea that the teacher’s role is not to share too much or too little information with students, but to ‘‘share essential information’’ (p. 12). The data analysis showed that in many other messages, the theory–practice bridge was built by both the preservice and inservice teachers. 7.2. Effectiveness of video case discussions

7. Discussion In this study, by analyzing the content of teacher discourse in response to a video case of mathematics instruction we documented

Although there is a burgeoning interest in the use of online and multi-media cases, the effectiveness of such media still remains unanswered in teacher education literature (Boling,

1166

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

2007; Lampert & Ball, 1998; Masingila & Doerr, 2002). In our context, the video case was an effective tool because it depicted a real mathematics classroom, and preservice and inservice teachers were able to visit the case electronically and discuss asynchronously. The video case allowed the participants to see the complexity of the classroom teaching in greater detail than a written case possibly allows. It was particularly a great asset for preservice teachers to see how the written standards of mathematics teaching were enacted in the pedagogy of a veteran teacher. Our quality and effectiveness assessment showed that teachers could produce ‘‘sustainable’’ and ‘‘on-topic’’ discussions about different facets of classroom practice. One of the reasons for high sustainability rate and entirely on-topic contribution of participants may be the ‘‘anchored’’ structure of the forum. An anchor is ‘‘a topic that students find worthy of discussion’’ (Guzdial & Turns, 2000, p. 443). In our context, the video case along with the instructor’s prompts was an anchor in that students were asked to make their discussions based on what they watched on the video. 7.3. Inclusion of the video case teacher A unique characteristic of our research setting was the inclusion of video case teacher in the forum discussions. At the outset, we hypothesized that this could affect the discussions in two ways. First, the video case teacher could help the preservice and inservice teachers in the study to verify the truth of the claims they make about the video case. In other words, the participants could have a ‘‘member check’’ of their claims by the video case teacher. Second, the inclusion of the video case teacher could have adversely affected the preservice and inservice teachers’ contribution to the discussion because they might not have felt as comfortable as when the case teacher was not in the forum. Therefore, it might have been that some students refrained from putting their ideas into text. The analysis of Melissa’s contribution validated the first hypothesis to some degree. As previously presented, her most common response was confirmative in nature, followed by messages of explanatory, appreciative, and informative nature. These four major categories of responses helped students weigh the truth-value of their claims. In other words, responses that were confirmative and appreciative verified that the corresponding student idea or comment was approved by Melissa; responses which were explanatory helped teachers to understand why Melissa acted in a particular way. Finally, responses of an informative nature provided further details for students to evaluate, and perhaps to help them make new judgments, either expressed or unexpressed in the forum; but which helped them verify their initial position. In considering exchanges between the case teacher, and other participant teachers, we need to keep in mind that Melissa was protecting herself from the criticism. Therefore, the idea of ‘‘verification’’ was achieved only to the degree Melissa’s subjectivity allowed. Our second hypothesis, the effect of the video case teacher’s participation on the forthrightness of students’ messages was hard to test. As documented in the results section, we observed a wide range of student responses from being critical of to being concordant with the practices shown in the video case. For instance, two of the inservice male teachers, Tom and Ted, made blatant remarks about Melissa’s teaching. Therefore, we can say that there was not an absolute restraining effect of Melissa’s participation on everyone. Finally, the inclusion of the video case teacher also helped other participants realize what was going on behind the scene.

Many times, Melissa provided extra information about her teaching that was not readily observable in the video. The information Melissa provided helped participants realize the complexities of teaching. Often times, when we make comments about a teaching segment in a video, it would not be possible to consider every aspect by watching the video. The background information along with behind the scene descriptions helped the preservice and inservice teachers realize the difficulty of judging a teaching segment, in as much as helped them realize there are more things to consider than what can be observed.

8. Limitations and further suggestions While our results suggested that video case discussion have great potential to help teachers make stronger theory–practice connections, there are several limitations of our research. First, short duration and relatively small sample size of our study and the fact that only one video case included in our study limit us to make a stronger argument on the effectiveness of the video cases in fostering theory–practice connections. Second, one of the researchers was also the instructor of the classes where the data were collected. The researchers’ bias for the effectiveness of video cases in teacher education might have inadvertently influenced the data interpretation. Another limitation of our study is that our a priori code list derived from the two theoretical frameworks might have overlooked some features of the teacher discourse. However, by providing detailed descriptions of our codes and rich examples of participant responses, at the least, we tried to represent the most comprehensive picture of our data possible as the space allows us. Finally, since we did not interview the participants, we know very little about whether and how inservice teachers moved preservice teachers’ thinking or what preservice teachers learned from inservice teachers. Given the limitations listed above, further research should utilize larger sample sizes and a wide variety of cases that reflect different facets of classroom teaching. Furthermore, alternative methods and theoretical lenses should be employed to capture the varying features of teacher interactions and resulting learning outcomes. Particularly, how preservice teachers benefit from interacting with inservice teachers, including the case teacher, should be studied more in depth. We discussed the potential benefits of the inclusion of the video case teacher in the forum discussions. However, our results remain inconclusive because we have not had a chance to interview our participants about the inclusion of the case teacher and the study was limited in duration. More research is needed to understand the pros and cons of the inclusion of the video case teacher in the discussions. Finally, in our research, the instructor provided discussion prompts, and the online discussions were centred on those prompts. This was a strategy to ‘‘anchor’’ student discussions. We suggest that future research should consider studying online video case discussions without the facilitation of the course instructor to see if the participants still build the theory–practice connections. Acknowledgement The authors equally contributed to this research. The authors thank to anonymous reviewers whose insightful comments helped improve the quality of the article.

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

Appendix A

Appendix C (continued) Coding categories Teacher as facilitator

Instructor’s discussion prompts

1st prompt

2nd prompt

Please, discuss Melissa’s mathematics lesson by using the Making Sense framework. As you see, this is a pretty general question. Thus, you may reflect on particular features of each dimension We will discuss this video one more week, by Monday midnight. This time, please analyze the teaching of Ms Melissa by using the NCTM principles and standards as your framework, like we did before.. We analyzed Ms. Melissa’s teaching by using the ‘‘dimensions of classrooms’’ in Making Sense.. This time, we will use the NCTM principles and standards. Specifically, Do you see any implementations of the standards in this video?

Teacher as assessor

Teacher as instructional decision maker

Appendix B Examples to multiple codings

Sample message

Assigned codes

Although I believe Melissa did hit all the standards that Polly stated, I do not believe that she properly mastered each area. It seemed as if her connection from each section didn’t match up to me. She stated that this was a review of doubling from a previous lesson, and she wanted to introduce them thinking algebraically and using symbols. She introduced the story about doubling, then a T chart, next the students worked on a tripling T chart. I can see the connection there, but after that I am lost. She had the students subtracting double digits groups and then doing place values. So to me, it seems as if her focus and connections were all over the place. In addition, she did communicate with the students and vice versa, but I’m not sure we can be positive that the communication that took place reinforced the learning taking place. The students simply shared their findings, and I didn’t feel that the teacher probed them to find out if they really grasped the concepts. Pearl The use of manipulatives also allowed the students to help make the connection between the story and the chart discussions. Melissa exposed the students to various approaches to the function. Her classroom climate and group work helped the students make the connection. The student interaction with each other on their ideas was a good communication. Phil

Teacher as manager Teacher as instructional decision maker Teacher as facilitator

Student understanding

Standards

Tools Classroom culture

Integration

Appendix C Classroom culture

Sample codes

Coding categories Teacher Roles Teacher as manager

1167

Sample codes Melissa, I was just wondering why the lesson went from 12:50 until 2:45. Is that your normal time alloted for your Math lessons, or did you change your schedule for that day? I’m currently doing field work in a third grade classroom, and it seems to me that the students would never be able to work that long on a subject, let alone math. How do you keep your students engaged in the task for a long period of time? Any comments you could offer would be greatly appreciated. Pearl

Equity and accessibility Tools

Sample codes The role of the teacher is so important and comes from how the teacher views his or her position and purpose in the classroom. I think Melissa does a great job of combining the role of ‘‘sage on the stage’’ with ‘‘guide on the side’’. She gives the students some information and starts them thinking. Then she spends of lot of time directing and guiding the thinking so that the students discover and ‘‘own’’ the knowledge they gain. It’s so much more valuable to them when they construct it themselves. Tirisha Wonderful Polly! I like how you picked up on the informal assessment. I think that teachers need to be doing some kind of assessment at all times. It helps us know what we need to do next. I would hope that most of it would be informal. I also noticed that Melissa give adequate wait-time. This was evident when she was asking questions during the story and also when she was working with the individual students at their desks. Paul The two that really seemed to stand out to me were communication and problem solving. Melissa really promotes a lot of problem solving in her classroom. Even if the students are having trouble coming up with the correct answer, she really tries to push them into figuring out a method of reasoning on their own. She never gives the students the answer that she is looking for, but tries to give them clues in the direction that she wants them to go. She also encourages communication in her classroom, which I believe to be a key element in a math class. Students need to be able to discuss with one another about the ways that they go about figuring things out. Polly The children were actively engaged in problem solving. They were asked to explain their reasoning for their answers. When the students were at their desks working, a young lady found a pattern. The teacher asked her to communicate her findings to the whole class. The fact that she could communicate it effectively means that she understood what was being taught. Palmira I think a few standards are being met. First communication is one of the NCTM standards and there is clear evidence of communication from the reading of the story to the children working with the manipulatives. Reasoning is also evident in the lesson. The students had to use reasoning skills to come up with answers because Melissa was not just giving them the answers she was like a guide, which intern made them have to stop and think about it. Problem solving is also a a standard and even though they didn’t not reach the answer it was clear evidence of problem solving or they would not have even came up with the answers they did achieve whether right or wrong. Melissa’s lesson covered a lot of standards! Precious I agree that using a book to introduce the lesson was a good idea. I just taught a lesson today about doubles and if I had viewed this video before hand, I could have used this same idea. I think that learning should be across all subjects. Children should see how the subjects they learn in class interact with each other and that they are not all separate unto themselves. Palmira I agree with Priscilla. I believe that work stations are a wonderful way to get students engaged in the activities. They are moving away from their desks, interacting with other students, and just being able to move around and do something different. I think it would be difficult to do this with every class, because some classes have not developed their classroom nature or social culture, which would allow them to interact with each other and at stations. Once students begin to respect each other and use tools to learn mathematics, I believe a set up like this can be very successful in influencing student learning and communication. Pearl I think that Melissa treated all students the same. She did not expect any less from one student than she did from another. There was certainly equity in her classroom. Palmira Tools are a vital part of a lesson as was demonstrated in Melissa’s lesson. If used properly they can provide a way in communicating with others and tools can make the child think outside the box. I hope more teachers use this type of teaching so all our kids can understand math. Pamela

1168

Y. Koc et al. / Teaching and Teacher Education 25 (2009) 1158–1168

References Arellano, E. L., Barcenal, T. L., Bilbao, P. P., Castellano, M. A., Nichols, S., & Tippins, D. J. (2001). Case-based pedagogy as a context for collaborative inquiry in the Philippines. Journal of Research in Science Teaching, 38, 5. Bencze, L., Hewitt, J., & Pedretti, E. (2001). Multi-media case methods in preservice science education: enabling an apprenticeship for praxis. Research in Science Education, 31, 191–209. Boling, E. C. (2007). Linking technology, learning, and stories: implications from research on hypermedia video-cases. Teaching and Teacher Education, 23, 189–200. Bonk, C. J., Wisher, R. A., & Lee, J. Y. (2003). Moderating learner-centred e-learning: problems and solutions, benefits and implications. In T. S. Roberts (Ed.), Online collaborative learning: Theory and practice (pp. 54–85). Hershey, PA: Idea Group Publishing. Brophy, J. (2004). Using video in teacher education. In: Advances in research on teaching, Vol. 10. Amsterdam:: Elsevier. Butler, M. B., Lee, S., & Tippins, D. J. (2006). Case-based methodology as an instructional strategy for understanding diversity: preservice teachers’ perceptions. Multicultural Education, 13(2), 20–26. De Wever, B., Schellens, T., Valcke, M., & Van Keer, H. (2006). Content analysis schemes to analyze transcripts of online asynchronous discussion groups: a review. Computers and Education, 46, 6–28. Guzdial, M., & Turns, J. (2000). Effective discussion through a computer-mediated anchored forum. Journal of the Learning Sciences, 9(4), 437–469. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann. Hong, L. T. (1993). Two of everything: A Chinese folktale. Morton Grove, IL: Albert Whitman & Company. Jay, J. (2004). Variations on the use of cases in social work and teacher education. Journal of Curriculum Studies, 36(1), 35–52. Kilpatrick, J., Martin, G., & Schifter, D. (2003). A research companion to principles and standards for school mathematics. Reston, VA: NCTM. Lampert, M., & Ball, D. L. (1998). Teaching, multimedia, and mathematics: Investigations of real practice. New York, NY: Teachers College Press. Lundeberg, M. A. (1999). Discovering teaching and learning through cases. In M. A. Lundeberg, B. B. Levin, & H. L. Harrington (Eds.), Who learns what from cases and how? The research base for teaching and learning with cases (pp. 3–24). Mahwah, NJ: Lawrence Erlbaum Associates. Lundeberg, M. A., & Levin, B. B. (2003). Prompting the development of preservice teachers’ beliefs through cases, action research, problem-based learning and technology. In J. Raths, & A. McAninch (Eds.), Teacher beliefs and classroom performance: The impact of teacher education (pp. 23–42). Greenwich, CT: Information Age Publishing. Lundeberg, M. A., Levin, B. B., & Harrington, H. L. (1999). Who learns what from cases and how? The research base for teaching and learning with cases. Mahwah, NJ: Lawrence Erlbaum Associates.

Manouchehri, A. (2002). Developing teaching knowledge through peer discourse. Teaching and Teacher Education, 18, 715–737. Masingila, J. O., & Doerr, H. M. (2002). Understanding pre-service teachers’ emerging practices through their analyses of a multimedia case study of practice. Journal of Mathematics Teacher Education, 5, 235–263. Mayo, J. A. (2002). Case-based instruction: a technique for increasing conceptual application in introductory psychology. Journal of Constructivist Psychology, 15(1), 65–74. Mayo, J. A. (2004). Using case-based instruction to bridge the gap between theory and practice in psychology of adjustment. Journal of Constructivist Psychology, 17(2), 137–146. McGraw, R. H., Lynch-Davis, R. K., Koc, Y., Kapusuz-Budak, A., & Brown, C. A. (2007). The multimedia case as a tool for professional development: an analysis of online and face-to-face interaction among mathematics pre-service teachers, in-service teachers, mathematicians, and mathematics teacher educators. Journal of Mathematics Teacher Education, 10(2), 95–121. Merseth, K. K. (1992). Cases for decision making in teacher education. In J. H. Shulman (Ed.), Case methods in teacher education (pp. 50–63). New York: Teachers College Press. Morson, G. S. (2003). The aphorism: fragments from the breakdown of reason. New Literary History, 34, 409–429. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Nemirovsky, R., & Galvis, A. (2004). Facilitating grounded online interactions in video-case-based teacher professional development. Journal of Science Education and Technology, 13(1), 67–79. Neuendorf, K. A. (2002). The content analysis guidebook. Thousand Oaks, CA: Sage Publications. Schrader, P. G., Leu, D. J., Jr., Kinzer, C. K., Ataya, R., Teale, W. H., Labbo, L. D., et al. (2003). Using Internet delivered video cases, to support preservice teachers’ understanding of effective early literacy instruction: an exploratory study. Instructional Science, 31, 317–340. Seago, N. (2004). Using video as an object of inquiry for mathematics teaching and learning. In J. Brophy (Ed.), Using video in teacher education: Advances in research on teaching, Vol. 10 (pp. 259–286). Amsterdam: Elsevier. Senk, S. L., & Thompson, D. R. (2003). Standards-based school mathematics curricula: What are they? What do students learn? Mahwah, NJ: Lawrence Erlbaum Associates. Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475–491. Titscher, S., Meyer, M., Wodak, R., & Vetter, E. (2000). Methods of text and discourse analysis. (B. Jenner, Trans.). Thousand Oaks, CA: Sage. Weber, R. P. (1990). Basic content analysis. Newbury Park, CA: Sage. Wells, C. G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. Cambridge, UK/New York, NY, USA: Cambridge University Press. Whittaker, S., Terveen, L., Hill, W., & Chemrny, L. (1998). The dynamics of mass interaction. In S. Poltrock, & J. Grudin (Eds.), Proceedings of CSCL ’98 (pp. 257–264). New York, NY: ACM.