Pedagogical content knowledge as reflected in teacher–student interactions: Analysis of two video cases
Abstract
Despite the theorized centrality of pedagogical content knowledge (PCK) for teaching, we have little evidence of the relationship between PCK and students' learning and know relatively little about how to help teachers to develop PCK. This study is a preliminary attempt to address these gaps in our knowledge of PCK through exploration of two German physics teachers' classroom instruction in consecutive lessons on optics. We show how video analysis can be used to gather evidence for one aspect of teachers' PCK: their use of content knowledge in interactions with students. We identify three potentially important characteristics of this aspect of PCK: flexibility, richness, and learner-centeredness. By contrasting teachers with high and low gains in student knowledge and interest, we explore potential mechanisms by which this aspect of PCK might affect student outcomes. Because German teacher preparation programs emphasize content more than pedagogical knowledge, these cases contribute to our understanding of the support that teachers with strong content knowledge may need in translating this knowledge into a form useful for teaching.Fachdidaktisches Wissen ist aus theoretischer Sicht besonders zentral für das Unterrichten. Aus empirischer Sicht gibt es bislang allerdings noch wenig Evidenz für den Einsatz fachdidaktischen Wissens während des Unterrichtens und seine Bedeutung für das Lernen von Schülerinnen und Schülern. Außerdem wissen wir wenig darüber, wie Lehrpersonen über die Zeit fachdidaktisches Wissen entwickeln. Diese Studie ist ein Versuch, diese Wissenslücken zum fachdidaktischen Wissen von Lehrpersonen zu bearbeiten. Dabei wird exemplarisch der Unterricht von zwei deutschen Physiklehrern in aufeinanderfolgenden Stunden zum Thema Optik untersucht. Die Studie zeigt wie Videoanalysen genutzt werden können, um Belege für einen Aspekt des fachdidaktischen Wissens der Lehrpersonen zu sammeln: Ihre Nutzung von inhaltlichem Wissen in der Interaktion mit den Schülerinnen und Schülern. In dieser Studie werden drei potentiell wichtige Charakteristika dieses Aspekts des fachdidaktischen Wissens identifiziert: Flexibilität, Reichhaltigkeit und Schülerorientierung. Durch die Gegenüberstellung von Lehrpersonen mit hohem und niedrigem Wissens- und Interessenzuwachs wurden potentielle Mechanismen untersucht, durch die dieser Aspekt des fachdidaktischen Wissens die Lernergebnisse von Schülerinnen und Schülern beeinflussen kann. Die Lehrerausbildung in Deutschland betont das inhaltliche Wissen stärker als das fachdidaktische Wissen. Die ausgewählten Fälle beschreiben, welche Unterstützung Lehrpersonen mit einem hohen fachlichen Wissen benötigen, um dieses Wissen so zu verändern, dass es für das Unterrichten genutzt werden kann. © 2012 Wiley Periodicals, Inc. J Res Sci Teach 49: 1211–1239, 2012
In countries around the world, alarms have been raised about students' relatively low levels of achievement and interest in science (e.g., National Academy of Sciences, National Academy of Engineering, & Institute of Medicine, 2007; Organisation for Economic Co-operation and Development, 2007). Fostering science achievement and interest is viewed by many as critical to a nation's future. From an economic perspective, the next generation of scientists and engineers will be responsible for innovations that drive a nation's economy. To benefit from these innovations, citizens and workers need ever higher levels of scientific and technological sophistication. In addition, advances in science and technology are critical for improving standards of living and for providing solutions to challenges of the modern world, including those related to health, energy, environment, and security. Decisions about these issues and associated trade-offs require a citizenry equipped with the scientific knowledge to consider arguments and contribute to debates.
While many factors may contribute to students' achievement and interest in a particular school subject, teachers have a major impact on these outcomes (e.g., Akiba, LeTendre, & Scribner, 2007; Osborne, Simon, & Collins, 2003). The United States (US) National Research Council (NRC) has stated, “Teachers make a difference. Indeed, of all the factors that education leaders can control, the quality of teaching has perhaps the greatest potential effect” (2010, p. 9). However, efforts to link teacher characteristics such as test scores, subject matter degrees, or coursework to student achievement have had only modest success (e.g., Wayne & Youngs, 2003). A possible explanation for these findings may be that measures designed as proxies for teacher knowledge do not capture the aspects of teacher knowledge that most influence student learning (e.g., Wilson, Shulman, & Richert, 1987). In particular, pedagogical content knowledge (PCK; Shulman, 1986) has been proposed as an important aspect of teachers' knowledge. In an edited volume on PCK, Baxter and Lederman stated, “It is clear that teacher educators and researchers have identified pedagogical content knowledge as a critical component of the knowledge needed to teach” (1999, p. 147).
Despite the theorized centrality of PCK, we have little evidence of the relationship between PCK and students' learning (Abell, 2008; Baxter & Lederman, 1999; Shulman, 1999), and we know relatively little about how to help teachers to develop PCK (Lee, Brown, Luft, & Roehrig, 2007). In this article, we report on a preliminary attempt to address these gaps in our knowledge of PCK through exploration of two German physics teachers' classroom instruction on optics. By contrasting teachers with high and low gains in student knowledge and interest, we explore potential mechanisms by which PCK might affect student outcomes. Because German teacher preparation programs emphasize content more than pedagogy (Bauer et al., 2010), these cases contribute to our understanding of the support that teachers with strong content knowledge may need in translating this knowledge into a form useful for teaching.
This article starts with an exploration of what is known about PCK—both its impact on student achievement and motivation and methods for accessing and supporting teachers' development of this often tacit form of knowledge. This review of the literature serves as the foundation for our in-depth look at instruction in two German physics classrooms. The second section of the article describes the methods used in this study, including the context for our work and the methods used to analyze videos of classroom instruction. The third section presents results, including a comparison of the two teachers' use of physics content in classroom interactions with their students. The final section of the article provides a discussion of potential connections between characteristics of teachers' use of content knowledge in classroom interactions and students' knowledge and interest. It also describes limitations of the study and posits possible contributions in terms of efforts to capture PCK, to link teachers' PCK and student outcomes, and to support the development of teachers' PCK.
Pedagogical Content Knowledge (PCK)
Over the past few decades, researchers have turned from a focus on teachers' behaviors to a focus on teachers' knowledge and how that knowledge influences instructional decisions (Ball, 1991; Peterson, Fennema, Carpenter, & Loef, 1989). Since its introduction, PCK has generated much interest as a potentially key component of teachers' knowledge. As explored below, there is good theoretical reason to believe that teachers' PCK will have a significant impact on students' achievement and motivation. Thus influencing teachers' PCK may be an effective means of addressing the recognized need to improve students' achievement and interest in science.
Teaching is more than knowing subject matter oneself and transferring that knowledge to others. Many people have had the experience of sitting in a lecture in which a brilliant scholar is unable to translate his or her expertise in a way that is comprehensible to novices. In his 1986 Educational Researcher article, Lee Shulman asked an important question about the relationship between subject matter knowledge and teaching: How do teachers draw upon “expertise in subject matter in the process of teaching” (p. 8)? He introduced the idea of PCK, the “particular form of content knowledge that embodies the aspects of content most germane to its teachability” (p. 9) to address this question. PCK is what allows excellent teachers to make disciplinary ideas comprehensible to non-experts. It distinguishes a teacher from disciplinary experts, as well as from colleagues who teach other subjects (Marks, 1990).
In the over two decades since PCK was defined (Shulman, 1986), there have been many attempts to characterize this type of knowledge (e.g., Carpenter, Fennema, Peterson, & Carey, 1988; Geddis, Onslow, Beynon, & Oesch, 1993; Grossman, 1990; Gudmundsdottir, 1995; Hashweh, 2005; Lee & Luft, 2008; Magnusson, Krajcik, & Borko, 1999; Marks, 1990; Park & Oliver, 2008; Veal & MaKinster, 1999). At the core of all characterizations of this construct are two key components: knowledge of student learning difficulties and knowledge of instructional representations (van Driel, Verloop, & de Vos, 1998). These components are thought to underlie teachers' instructional decision-making—from planning how best to present content to students to interacting with them in the midst of classroom instruction (Borko, Roberts, & Shavelson, 2008; Shulman, 1987).
The Impact of PCK on Student Outcomes
Whereas content knowledge alone might suffice in a transmission model of instruction, currently accepted theories of teaching and learning require complex interactions between content, teacher, and students that rely heavily upon teachers' PCK (e.g., Cochran, DeRuiter, & King, 1993; Geddis, 1993). A number of scholars have articulated valued instructional practices that are thought to be impacted by teachers' PCK and, thus, a rationale for the relationship between PCK and student achievement (Loughran, Milroy, Berry, Gunstone, & Mulhall, 2001; McDiarmid, Ball, & Anderson, 1989). Park, Jang, Chen, and Jung (2011) demonstrated a strong correlation between teachers' PCK (as measured with a paper-and-pencil test) and the reform-oriented nature of their teaching as measured by the Reformed Teaching Observation Protocol (RTOP).
In addition, Rohaan, Toconis, and Jochems (2010) make a direct argument for the impact of teachers' PCK on student attitudes in primary technology education.[The research findings] raise substantial questions about why the pedagogy of some science teachers is so unappealing to the majority of students, suggesting that, while science teachers may be knowledgeable about their subject, they are failing to achieve their primary task of establishing a range of varied learning opportunities and communicating their subject effectively. (p. 1068)
While PCK may be theorized to impact both student achievement and motivation, there is little direct evidence of the relationship between teachers' PCK and student outcomes (Baxter & Lederman, 1999; Shulman, 1999). A study in mathematics (Peterson et al., 1989) demonstrated a relationship between some components of PCK and student achievement in a particular area of the mathematics curriculum. In this study, PCK was operationalized in terms of three competencies related to students' engagement with addition and subtraction word problems: ability to compare the relative difficulty of two word problems, ability to use observations of students' solutions to a set of word problems to predict how they would “solve related problems” (p. 10), and ability to predict their own students' answers to word problems (in terms of both correctness and solution strategy). A study in science provided “slight evidence of a relationship between teacher pedagogical content knowledge and student knowledge” (Magnusson, 1991, abstract) in the area of heat and temperature. This study used interview data to assess teachers' PCK and students' content knowledge. More recently, two studies have used statistical analyses to link gains in students' learning of science to teachers' PCK (Roth et al., 2011) and to increases in teachers' PCK (Kanter & Konstantopoulos, 2010). The former study assessed teachers' PCK using a video analysis task. Teachers' “analytical comments about the science content, the teaching, and/or the students” were used to rate teachers' PCK in terms of two dimensions: “Science Content Storyline” and “Student Thinking” (Roth et al., 2011, p. 126). The latter study rated teachers' PCK on the basis of “detailed written analys[es] of a video tape of their teaching” (Kanter & Konstantopoulos, 2010, p. 864). In particular, researchers were interested in “episodes” (p. 864) that included the identification of evidence of student thinking, an interpretation of the student thinking, and a response that would either confirm the diagnosis of student thinking or address the student thinking. This study also examined student attitudes towards science but found no statistically significant correlation between increases in teachers' PCK and improvements in students' attitudes. All of these authors acknowledge limitations of their studies and call for additional work to explore the relationship between PCK and student achievement and/or motivation.
Characteristics of PCK
Efforts to move beyond theoretical considerations of PCK depend upon methods for (a) capturing and describing specific examples of PCK and (b) influencing teachers' PCK. However, a number of characteristics of PCK complicate this work.
First, like many forms of teacher knowledge, PCK is difficult to articulate. Yet sharing knowledge requires some means of representing that knowledge to others (Geddis et al., 1993; Hiebert, Gallimore, & Stigler, 2002; Shulman, 1987). PCK—as knowledge that influences practice—is often tacit, largely because practice does not require its articulation (Loughran, Mulhall, & Berry, 2004). Teachers are often unaware of knowledge they use to make instructional decisions, and day-to-day discussions of teaching tend to center around practices, rather than the knowledge and reasoning underlying them. Thus because teaching itself does not require articulation of PCK, teachers may not possess a shared language with which to communicate this knowledge to each other, to researchers, and to those learning to teach (Baxter & Lederman, 1999).
Second, Shulman (1987) describes pedagogical reasoning—the way that PCK is translated into practice—as including both adaptation (considering general characteristics of learners) and tailoring (adjusting to specific learners). Yet most studies of PCK focus upon generalizable descriptions and, thus, only on knowledge underpinning the former type of reasoning. A mathematics study documented teachers' knowledge of their own students' problem-solving strategies (Peterson et al., 1989)—knowledge underlying the tailoring process; however, similar research has not been conducted in science to date. Studying PCK involves a balance between the general and specific characteristics of this knowledge; while general knowledge of student difficulties and instructional representations may support teachers' classroom interactions, what matters in terms of students' instructional experiences is “PCK-in-action” (Janík & Miková, 2006).
Third, because PCK is involved in translating specific content knowledge into a form that is meaningful to particular students, it is both topic-specific (e.g., Magnusson et al., 1999; McDiarmid et al., 1989; Park & Chen, 2012; van Driel et al., 1998) and context-dependent (e.g., Cochran et al., 1993; Grossman, Wilson, & Shulman, 1989). “[PCK] is bound up—and recognizable—in a teacher's approach to teaching particular content” (Loughran et al., 2001, p. 290). Thus to characterize the knowledge required to teach a subject such as physics, one must consider the PCK required to teach particular concepts in mechanics, electromagnetism, etc. In science we have very few descriptions of PCK for particular topics (Geddis et al., 1993; Loughran et al., 2004; Magnusson et al., 1999; van Driel et al., 1998) and in different classroom contexts. This work may be particularly important, given Hashweh's (2005) proposition that theoretical discussions of PCK may be at an impasse. Researchers have posited slightly different ways of conceptualizing PCK; specific descriptions of PCK may be required to advance and refine our understanding of this construct.
Finally, PCK is thought to be or to result from the transformation of other types of knowledge—particularly content knowledge (e.g., Geddis et al., 1993; Magnusson et al., 1999; Shulman, 1987). There is little direct evidence of how PCK develops (Clermont, Borko, & Krajcik, 1994), and, thus, what experiences and background knowledge might be most important in supporting novice teachers' development of PCK. While many researchers contend that content knowledge is a necessary prerequisite for the development of PCK (e.g., Daehler & Shinohara, 2001; van Driel et al., 1998), others (Magnusson et al., 1999; Marks, 1990) have posited that there may be multiple pathways to developing PCK: Teachers with strong subject matter knowledge and those with strong general pedagogical knowledge may each build upon their existing knowledge to construct PCK. However, these researchers do not posit mechanisms by which this construction occurs nor strategies for supporting teachers with different background knowledge. In addition, although some research indicates that teacher preparation programs lay an important foundation for teachers' development of PCK (Grossman, 1990), other work indicates limited impact for such programs (van Driel et al., 1998). Most researchers report that classroom experience is essential for teachers to develop PCK (e.g., Adams & Krockover, 1997; Cochran et al., 1993; Grossman, 1990; van Driel et al., 1998). While efforts to develop teachers' PCK are important in their own right, a better understanding of how PCK develops may help to provide a deeper conceptualization of the nature of this knowledge.
Overview of the Study
The study described in this article was framed within this context of our understanding of PCK. At its core, this study is an attempt to explore the relationship between teachers' PCK and student achievement and motivation. In particular, we chose contrasting cases—classrooms with high and low gains in student knowledge and interest—and asked the following question: What differences in the use of content knowledge during classroom interactions can be discerned between a teacher whose students made high gains (in knowledge and interest), as compared to a teacher whose students made low gains? We chose to focus on use of content knowledge as an important subset of PCK, visible to a large degree in teachers' classroom interactions with students. This is consistent with Shulman's focus on “the management of ideas within classroom discourse” (1987, p. 1) and with the construct of content knowledge for teaching, defined by Ball, Thames, and Phelps (2008) as a subset of PCK. Mathematical knowledge for teaching has been demonstrated to be significantly related to gains in student achievement (Hill, Rowan, & Ball, 2005). Thus there is reason to believe that this aspect of PCK is worth examining in more depth.
In this study, we focus on “PCK-in-action” (Janík & Miková, 2006). This is consistent with Shulman's (1987) emphasis on the practical importance of PCK: that its utility “lies in its value for judgment and action” (p. 14). We are aware of the argument that observations of classroom events cannot provide a complete portrayal of PCK (e.g., Baxter & Lederman, 1999; Loughran et al., 2004) and of Kennedy's (2010) concerns about “attribution error” when inferring teachers' knowledge from their behavior. Therefore, we are not claiming to be able to capture all aspects of PCK in this manner; rather, we are interested in identifying aspects of PCK that might be captured through classroom video. We agree with Baxter and Lederman (1999) that multiple approaches are likely needed to fully capture teachers' PCK and view observations as a particularly important approach to include in such a multi-pronged effort. In light of the features of PCK discussed above, we believe that observations have some important advantages over other methods for accessing teachers' PCK. First, observations do not require teachers' articulation of this often tacit form of knowledge. Second, observations capture PCK where it matters most: in its influence on teachers' work with their students. In doing so, observations reflect PCK as it is used in practices associated with teaching, rather than practices that are further removed from the classroom—such as interviews (e.g., Clermont et al., 1994; Lee et al., 2007; Magnusson, Krajcik, & Borko, 1994) and paper-and-pencil assessments (e.g., Hill, Ball, & Schilling, 2008;1 Park, Chen, & Jang, 2008). Third, considering PCK as it is used in teachers' own classrooms honors the context-specific nature of PCK. Therefore, while acknowledging the potential limitations of observations as a method for capturing teachers' PCK, we believe that its affordances are worth exploring.
In addition to our choice to focus on classroom observations as a source of evidence of teachers' PCK, two additional features of the study were responsive to our knowledge of PCK, as described above. First, we examined classroom videos in which teachers and students were engaged in a study of optics. Thus we attended to the topic-specific nature of PCK and hoped to contribute examples of PCK in a specific area of the physics curriculum that has received little attention to date. Second, German teacher preparation programs—particularly for teachers who will be placed in the highest level of secondary school—place heavy emphasis on content. The teachers in this study serve as examples of how teachers with strong content knowledge use that knowledge in their classroom interactions with students.
Methods
Context
The context of this study is important due to both the nature of PCK as a theoretical construct and the specific design of our study. First, PCK is context-specific, and its development may depend upon the nature of teachers' preparation and foundational content and pedagogical knowledge. Second, the design of this study is dependent upon the selection of teachers who represent variation with respect to gains in student knowledge and interest but who are similar in other respects. The context is described at several levels: the national level (to provide general context with respect to teacher preparation and teachers' foundational knowledge), the level of the larger study from which our data was selected (to provide context for the data collection and selection of cases for the current study), and the classroom level (to provide context with respect to the specific teachers and students involved in this study).
National Context
This study is situated in German physics classrooms. The German school system differentiates three levels of secondary school, leading to different qualifications for further education. The lowest and middle teaching levels (Hauptschule and Realschule, respectively) are geared towards vocational education, while the highest teaching level (Gymnasium) leads to a general qualification for university entrance. Although details of teacher preparation programs in Germany depend upon the federal state, some characteristics are common nationwide. Teacher education takes place according to the candidate's desired level of secondary school. The first phase takes place at the university where, particularly for those preparing to teach at the Gymnasium level, there is a strong emphasis on content knowledge. The second phase of teacher preparation is school-based, involving teaching in schools and reflections on those experiences. While this phase places greater emphasis on pedagogical aspects of teaching, overall, content knowledge plays a central role in German teacher preparation programs. There is great concern in Germany that this emphasis does not support teachers in integrating content and pedagogical knowledge and that this may be responsible for students' low achievement and interest in science (Terhart, Bennewitz, & Rothland, 2011).
The study of German teachers provides an important comparison to work conducted with US teachers because of differences in teacher preparation in the two countries (Prenzel & Seidel, 2009). German teachers typically have strong content background, while US teacher preparation programs place more emphasis on pedagogy (e.g., Schmidt et al., 2007).
Video Study Context
The two cases analyzed in the current study were selected from the IPN Video Study (Seidel & Prenzel, 2006; Seidel et al., 2007), which sought to capture a representative sample of German ninth grade physics instruction. The goal of the IPN Video Study was to investigate German physics instruction and its effects on students' cognitive and motivational-affective learning outcomes. Fifty teachers and their 1,249 students in four different federal states in Germany volunteered to participate after their schools had been randomly selected for inclusion in the study. Figure 1 illustrates the research design of the IPN Video Study.
Research design of the IPN Video Study. From The Power of Video Studies in Investigating Teaching and Learning in Classrooms (p. 167), by T. Janík & T. Seidel (Eds.), 2009, Münster, Germany: Waxmann. Copyright 2009 by Waxmann Verlag GmbH. Reprinted with permission.
During the 2002/2003 school year, a teaching unit of two periods (approximately 80–90 minutes in total) on either optics or mechanics was video-recorded in each classroom, according to standardized guidelines (Seidel, Dalehefte, & Meyer, 2005). Classes were video-recorded during normally scheduled instruction on one of the two topics; teachers were asked to introduce the topic as usual. Directly after the video-recording, teachers were asked to briefly evaluate the recorded lessons. Most of the teachers reported the lesson and the students' behavior to be representative of their everyday lessons.
Pre-/post-measures of students' knowledge and interest were administered at the beginning and end of the school year. Identical questionnaires were used for the pre- and post-tests. The knowledge scale included 16 dichotomously scored standardized national and international (TIMSS released) items focused on reflection and refraction (optics). Moderate values of Cronbach's alpha (α = 0.56 pre-test; α = 0.67 post-test) were obtained for the optics knowledge subscale (Rimmele et al., 2005). The interest scale was based upon earlier work by Häussler and Hoffmann (2000). In the IPN Video Study, five Likert-type items (1 = very low interest; 5 = very high interest) were used to assess students' interest in topics such as “the functioning of a telescope, microscope, or a camera.” Cronbach's alpha values for the pre- and post-test (α = 0.65 and 0.71, respectively) indicated moderate reliability for the optics interest subscale (Rimmele et al., 2005). Gains in knowledge and interest were used to select classrooms for inclusion in the current study.
Additional measures provided information that was used to evaluate the comparability of the two classrooms selected for this study. Four Likert-type items used to assess students' physics self-concept (e.g., “I have a talent for physics”) were included on the pre-/post-tests. Reliabilities (α = 0.86 pre-test; α = 0.84 post-test) were acceptable for this scale (Rimmele et al., 2005). In addition, the questionnaire that students completed when their classrooms were video-recorded included a test of cognitive abilities (Kognitiver Fähigkeitstest for 4th–12th Grade; Heller & Perleth, 2000). For the IPN Video Study sample, the Cronbach's alpha value of 0.84 indicates acceptable reliability (Rimmele et al., 2005).
At the end of the school year, teachers completed a questionnaire that included Likert-type questions about their domain-specific theories and beliefs about science teaching and learning as well as questions about their instructional practices throughout the school year. These two scales were each further divided into four subscales. Supporting Information Table 1 provides a description of each scale/subscale along with the number of items and Cronbach's alpha for the IPN Video Study sample.
Case Study Classrooms
A case study design was selected in order to “focus on understanding the dynamics present within single settings” (Eisenhardt, 2002, p. 8). We were interested in a detailed exploration of content-based interactions between teachers and students. Because we posited a relationship between these interactions and the development of students' knowledge and interest, we selected two classrooms that displayed contrasting patterns of knowledge and interest development over the school year. While this was our primary selection criterion, within the relatively small set of classrooms exhibiting either high gains in both knowledge and interest or low gains in both knowledge and interest, we selected two that were (a) located in the same geographical location and type of school; (b) as similar as possible in terms of student and teacher characteristics; and (c) video-recorded during lessons with similar structure and on the same topic (optics).
Our two cases are ninth grade physics classrooms at the Gymnasium level. Both are located in the federal state of Baden-Wuerttemberg, which is located in the southwestern part of Germany and is known for its high-achieving school system (Prenzel et al., 2005). Details about the students, teachers, and lessons are presented below. We note that, while there are many similarities in these characteristics, it was impossible to identify two classrooms that were perfectly matched on all relevant variables. This limitation is discussed in more detail below.
Students
Figure 2 displays the optics knowledge and interest development for all 50 classrooms included in the IPN Video Study, based upon aggregated person parameters for each classroom. Each teacher in the sample is represented by a square, with highlighting used to indicate the two teachers selected for inclusion in the current study.2 The graph on the left shows students' knowledge of optics, with the x-axis representing pre-test estimates and the y-axis representing post-test estimates. The line represents no change in knowledge of optics from pre- to post-test. Thus Martin's students had virtually no change in knowledge from pre- to post-test, while Peter's students made relatively large gains. The graph on the right shows students' interest in optics. Peter's students became slightly more interested in optics over the course of the year, while Martin's students displayed a small decrease in interest, typical of other classrooms in the IPN Video Study. The graphs also show that Martin's students started with greater knowledge of and interest in optics as compared to Peter's students; however, these differences were not statistically significant. Compared to other teachers in the IPN Video Study sample, Martin's students' gains (in both knowledge and interest) put him in the bottom quarter of the sample, and Peter's students' gains put him in the top quarter of the sample.
Optics knowledge and interest development of students in the 50 IPN Video Study classrooms. The two teachers selected for inclusion in the current study are highlighted.
These differences in students' development over the course of the school year need to be evaluated in light of other characteristics of the two classrooms. While students' cognitive ability was significantly higher in Peter's as compared to Martin's class (t = 2.19; df = 45; p = .03; d = 0.64), differences in students' physics self-concept were not. In Peter's class, 58.3% of the students were male; in contrast, Martin's class consisted of only 28.6% male students.
Teachers
The two teachers included in the current study were similar in a number of aspects. Both were younger than 45 years and therefore belonged to the younger half of the IPN Video Study sample. Peter had been teaching physics for 3 years and Martin for 4 years; this represented less teaching experience than the teachers in the IPN Video Study as a whole (M = 14.94; SD = 11.5). As noted above, details of teacher preparation programs in Germany are determined by the federal state. State-to-state differences in certification requirements mean that teachers generally teach in the state in which they were trained. Therefore, we can assume that Peter and Martin experienced similar teacher preparation with respect to relative emphasis on content and pedagogy (Bauer et al., 2010, 2011). Beyond their teacher preparation, Peter reported participating in a greater number of hours of professional development (“more than 60 hours”) than Martin (“10–30 hours”). In addition, the topics that the two teachers reported for these courses indicate that Peter's professional development may have been more directly related to his teaching of physics and mathematics. However, the lack of detailed information about these courses prevents detailed comparisons.
For the subscales in Supporting Information Table 1 (representing instructional practices and domain-specific theories and beliefs about science teaching and learning), there was only one statistically significant difference between Martin and Peter. While Martin's score on the structured teaching subscale (3.57 out of 5) was quite similar to that of the IPN Video Study sample as a whole (3.55), Peter scored significantly higher on this scale (4.14), indicating more frequent teacher-centered instructional practices. For all other subscales, differences between Martin's and Peter's scores were not statistically significant.
Lessons
In addition to contrasting gains in student knowledge and interest, the two classrooms in the current study were selected because of similarities in the lessons video-recorded. In both classrooms, an initial introduction to the topic preceded the two consecutive optics lessons that were recorded for the IPN Video Study. The total instructional time recorded in each classroom was just over an hour and a half (92 minutes in Peter's classroom and 95 minutes in Martin's classroom). In both classrooms, students were applying newly acquired understandings of optical components to analyze real optical devices. In Peter's classroom, students examined the optical components inside overhead projectors and worked to understand how they functioned to create an image. In Martin's classroom, students used lenses to explore how images are created by magnifying glasses and telescopes.
Although there was greater variation in the IPN Video Study sample as a whole, both lessons included in the current study followed a similar structure, including whole class discussions—characterized by a traditional Initiation–Response–Evaluation (IRE) pattern of discourse (Cazden, 2001)—as well short hands-on investigations. The presence of hands-on investigations in both classrooms may be particularly important, given recent findings about the impact of such activities on students' interest in science (Swarat, Ortony, & Revelle, 2012). The classroom talk in both classrooms consisted of approximately 60% teacher statements and about 40% student statements. Compared to other classrooms in the IPN Video Study, the proportion of student talk in these two classrooms was relatively high. Although many lessons in the IPN Video Study included hands-on investigations, this was not a uniform feature of the classrooms included in the larger study.
Analysis
All video-recorded instruction for each teacher was transcribed (in German) and then translated into English. The translations were verified by the second author, who had spent time working with English-speaking students in the US. The video-recordings were initially viewed by the first author without knowledge of why each teacher had been chosen for inclusion in the study (i.e., without knowledge of student-level data). Based upon a review of the PCK literature, impressions were recorded related to evidence of each teacher's PCK. These impressions were discussed with the research team (all three authors), and teachers' use of content knowledge in classroom interactions with students was selected as a subset of PCK that could be fruitfully explored with videos of classroom instruction.
Next, a more systematic exploration was undertaken, in which examples were identified in each video, reflecting either positively or negatively on the teacher's use of content in interactions with students. Finally, through discussion of these examples with the research team, a set of codes was developed to characterize teachers' use of content in classroom interactions. Through this grounded theory coding (Charmaz, 2000), three broad categories were identified: (1) flexible, (2) rich, and (3) learner-centered. We used flexible to describe teachers' recognition of students' unconventionally worded contributions and rewording of their own questions when students exhibited confusion. Rich was used to indicate teachers' use of examples and connections among multiple representations (e.g., words, formulas, and drawings) to enhance students' understanding of the content. A final category—learner-centered—was used infrequently but captured teachers' recognition of what piece(s) of content students need in order to grasp other pieces, as well as what content students find to be difficult and why.
Once these codes had been identified, data on gains in student knowledge and interest were revealed. We then followed an enumerative approach to data analysis (LeCompte & Preissle, 1993), identifying segments of video that reflected (either positively or negatively) on teachers' use of content in each of the three categories. Supporting Information Table 2 describes the types of instances that were coded. Associated subcodes (indicating specific manifestations) and rubrics (indicating quality) were also used to code/rate each instance. Further descriptions of the codes and subcodes are presented in the Coding section.
Our study relies upon investigator triangulation (Denzin, 1989) at all stages of the analysis process. In the final coding stage, the first author coded all of the videos, and the second author coded half of each teacher's videos. We discussed any discrepancies to agree upon a final characterization of each teacher's video, in terms of the identification of instances, subcodes, and quality ratings.
Coding
In this section, we describe our coding scheme in more detail. Supporting Information Tables 2–4 provide examples that further serve to illustrate how we analyzed the classroom videos. Additional examples are presented in the Results section below (to illustrate differences between the two classrooms).
Flexible Use of Content
As reflected in the positive and negative examples in Supporting Information Table 2, we identified two positive and four negative ways that this category played out in the classrooms. In recognizing instances, teachers recognized students' unconventionally worded contributions, either by rewording them at the time or by referring back to their ideas later in a discussion. In the other positive instantiation—rewording—teachers reworded their own questions to address student confusion. This subcode included rewording to clarify meaning, to focus on a more specific example, and to provide hints about relevant content. This subcode also included instances in which teachers helped students to approach multi-step problems by asking more direct questions about specific steps. Instances identified with the rewording subcode were also rated with a set of quality rubrics. As shown in Supporting Information Table 3, these rubrics were used to evaluate the clarity of the initial question, whether content-based scaffolding was provided, and the success of the rewording.
Negative instantiations of the flexible code were much less frequent and represented greater variety. In wording instances, teachers insisted on a particular wording of an idea, even when there was little apparent difference between a student's contribution and the desired statement. In not rewording instances, teachers did not reword questions even when students expressed confusion. When confronted with an incorrect student response, teachers repeated the question verbatim, moved on to interact with another student, or provided the answer themselves. Instances identified with this subcode were also rated on the clarity of the initial question (see Supp. Info. Table 3a). The simplifying subcode was used to identify instances in which the teachers reworded questions without preserving their original meanings. This allowed students to provide a correct answer without engaging with the content at the level required by the original question. (In contrast, in rewording instances, teachers retained their focus on the original question.) The simplifying instances were also rated on the clarity of the initial question and on students' responses (see Supp. Info. Table 3). The missed opportunity subcode was applied when students raised legitimate content-related concerns that were not taken up by the teacher.
Rich Use of Content
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Peter: In what kind of apparatus would you find a convex lens?
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S24: Camera.
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Peter: Exactly. And what does a convex lens do in a camera?
Learner-Centered Use of Content
The final category reflects the instructional decisions that teachers make on the basis of their understanding of how students develop knowledge in a particular domain (in this case, optics). Because this category is expected to be reflected in decision-making, rather than directly in classroom interactions, we do not view classroom video as an ideal way to capture this aspect of teachers' use of content. (This category is expected to be more visible in teachers' articulations of instructional decisions or in their reflections on practice.) However, important classroom interactions—both positive and negative—fell into this category. In positive instances, teachers demonstrated knowledge of how students develop understanding of content, including explaining why particular content is especially difficult to understand, emphasizing aspects of content that may be particularly challenging, or explaining a decision regarding the selection of content appropriate for students' level of understanding. In negative instances, teachers demonstrated a lack of knowledge of how students develop understanding of content, by setting tasks that students were not prepared to tackle and seeming not to recognize in advance that they would struggle.
Results
Initial Impressions
Before describing the results of our analysis, it is perhaps important to recount the first author's initial impressions of the two classrooms. We believe this is relevant because—as will be explored below—these impressions form an important contrast to the view of the two classrooms that was afforded by our coding and subsequent analysis. At the beginning of the study, the first author engaged in an initial viewing of the videos from the two classrooms. Without knowing how Martin's and Peter's students performed on the measures of optics knowledge and interest, she would have hypothesized that Martin's students would be more interested in his lessons and, thus, that they would learn more. Martin is a dynamic and personable teacher who appeared to have great rapport with his students. The real life examples that Martin brought to his students seemed appealing—for example, cheat sheets and being bleary-eyed in the morning. In contrast, Peter is much more reserved. His class simply seemed duller. His real life examples (traffic lights, overhead projectors) seemed less relevant to most students' interests.
Comparison Between the Two Classrooms
In contrast to these initial impressions, our coding and analysis revealed a quite different picture of the two classrooms. When we more closely examined how the teachers used content knowledge in classroom interactions with students, we saw how surface features were masking features with the potential to have a real impact on student outcomes and identified important differences between the two classrooms. These differences are summarized in Table 1.
| Characteristic of Teachers' Use of Content | Martin | Peter |
|---|---|---|
| Flexible use of content | ||
| Positive instantiations | Almost all (95%) rewording | 66% rewording; 34% recognizing |
| Rewording instances embedded in extended exchanges, with multiple attempts to elicit a particular response to the same initial question | Rewording and recognizing instances part of short exchanges used to sustain ongoing dialog between teacher and students | |
| Negative instantiations | More (22) negative instances identified | Fewer (13) negative instances identified |
| Almost all occurred as part of sequences with multiple attempts to elicit responses to particular questions, characterized by not rewording and simplifying | Most were wording instances that directly or indirectly conveyed that there was one right way of expressing physics ideas | |
| Most (80%) of the not wording and simplifying instances represented abandoned attempts to engage students with the content of the original question, while missed content and wording instances seemed to indicate a lack of recognition of physics content behind students' contributions | ||
| Rich use of content | Half as many (51) instances identified | Twice as many (106) instances identified |
| 15% of instances judged to represent deep connections | 59% of instances judged to represent deep connections | |
| 27% of instances judged to represent superficial connections; 10% of instances judged to represent unclear connections | Pattern of rich instances building from lower to higher level | |
| Real-life instances used to generate interest but not strongly supportive of students' understanding of physics content | ||
| Learner-centered use of content | Two (100%) negative instances in which a task was posed for which students were unprepared | Two (100%) positive instances in which particular ideas were acknowledged as more/less difficult |
Flexible Use of Content
In both classrooms, there was evidence of the teacher's flexible use of content knowledge. There were the same number of positive instances (39) identified in each classroom. However, comparing the two classrooms, there were important differences in the nature of these instances. In the vast majority of his positive instances (95%), Martin was rewording questions. In contrast, Peter both reworded his questions (66%) and recognized students' unconventionally worded contributions (34%). The latter instances often involved Peter's connections between students' contributions and the language of physics. For example, Peter asked students to describe a mirror that they found inside an overhead projector. A student said, “It was a semi-circle.” Peter restated this response to provide students with the correct scientific language by saying, “Semi-circle. So, it was not a—was not a smooth mirror. It was a domed mirror. There is a special term for that. This is a so-called concave mirror.”
The higher frequency of rewording in Martin's class may reflect his greater difficulty in wording questions that were comprehensible to students and in providing appropriate scaffolding to support their thinking. Across all of the rewording instances, 27% of Martin's original questions were judged to be incomprehensible (coded as 0 on the rubric in Supp. Info. Table 3a), and 68% did not include content-based scaffolding (coded as 0 on the rubric in Supp. Info. Table 3b). In contrast, none of the questions that Peter asked were judged to be incomprehensible, and only 38% of his rewording instances did not provide content-based scaffolding. Table 2 shows how an incomprehensible initial question led Martin to engage in a series of rewording instances.
| Instance Number | Transcript | Initial Question | Content-Based Scaffolding | Student Response |
|---|---|---|---|---|
| Martin: The image distance … would be just the focal distance. Assuming that the light arrived parallel. So, and now we just have to clarify whether we want to assume that the light arrives in parallel, what arrives? | ||||
| 1 | Martin: You have to judge that now. What would you say? | 0 | 0 | 1 |
| S11: The rays definitely do not arrive parallel | ||||
| 2 | Martin: Hm … Okay … look at this little area, this area is two and a half centimeters in diameter. Now imagine the light that comes from the lamp and falls through the opening—that is the lens—with this roughly two and a half centimeter diameter, can I view that as being parallel or not? | 1 | 1 | 1 |
| S14: No, not really | ||||
| 3 | Martin: Hm, well, I have a different opinion … I have to draw on the board, I believe … [sketches the situation on the board] So, look, I have the lens with this roughly two and a half centimeter opening just two meters away. And now we want to judge whether I can see the light that comes through as parallel. You are completely right when you say that the ray of light and it are not parallel. Anybody can see that. But that isn't what interests us. We are really only interested in the rays that fall through that little hole there … Can I see it as being parallel? | 1 | 1 | 1 |
| S19: It is so minimal | ||||
| 4 | Martin: What is minimal? | 1 | 0 | 2 |
| S19: The, ah, the not parallel-ness | ||||
| Martin: They, yes, exactly … Okay, I would say that for our circumstances, ah, it is almost okay to say that it is relatively parallel |
In addition to analyzing individual instances, we were able to get a further sense for how flexible instances contributed to the overall flow of the instruction in each teacher's classroom by looking across instances. Rewording instances sometimes occurred in clusters, with the code being applied repeatedly to a series of exchanges, as teachers made multiple attempts to elicit the correct answer to a single question. The length of these chains can be taken as a measure of teachers' struggle to make their questions comprehensible to students.
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Peter: What does a convex lens do? S20!
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S20: Yeah, it makes it smaller so the picture ah fits on the mirror.
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Peter: It makes it smaller. And now perhaps speaking more generally. What does a convex lens do? Think about the camera. What was the job there of the convex lens?
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S16: It focuses the picture.
In contrast, the discussion in Martin's classroom was characterized by more extended exchanges, in which Martin tried (through both positive and negative flexible instances) to elicit a particular response to the same initial question. Only three (<10%) of the rewording instances in Martin's classroom were single exchanges. The rest were embedded in 14 sequences of 2–9 flexible instances, 29% of which involved four or more attempts to get students to provide the correct answer. Table 2 shows an exchange with four consecutive rewording attempts. Note that these instances are connected through the coding scheme, such that, after the first instance, the initial question rating applies to reworded questions. Martin's initial question (“So, and now we just have to clarify whether we want to assume that the light arrives in parallel, what arrives?”) was unclear, and none of the students responded. He reworded the question without content scaffolding (instance 1), and although a student was able to respond, he did so incorrectly. Next, in instances 2 and 3, Martin provided some content scaffolding, helping students to imagine the situation (a lamp shining on a 2.5 cm lens from a distance of 2 m), first by describing it and then by drawing a sketch on the board. Finally, in instance 4, Martin asked a question to clarify the student's answer and received a satisfactory response (that the “not parallel-ness” is minimal). Therefore, through a series of rewording instances, Martin was able to elicit a correct answer from one of his students.
The average number of instances in a rewording sequence in Martin's classroom was 2.9 (SD = 2.0). As compared to Peter's classroom, a greater percentage of these of sequences ended with students being unable to answer the question satisfactorily: one-third of the rewording exchanges in Martin's classroom ended with negative flexible instances: Martin either simplified his original question so that students no longer had to engage with its content or provided the answer himself.
Overall, there were fewer negative flexible instantiations in Peter's classroom (13) as compared to Martin's (22). Three not rewording instances and one missed content instance occurred as part of rewording exchanges in Peter's classroom. The additional nine negative instantiations in his classroom were related to two types of wording, both associated with statements written on the overhead projector for students to copy into their notes. The first type was somewhat subtle and represented most (8 of 9) of the wording instances. In these instances, Peter referred to his notes in order to write exactly worded statements on the overhead projector. The second type occurred only once, in the wording example presented in Supporting Information Table 2, in which Peter—while recognizing that the student had provided a correct response—insisted upon a particular wording to be written on the overhead projector. Thus rather than relying upon language that he or his students used as part of a discussion, Peter (indirectly in the first type and directly in the second) conveyed that there was one right way of expressing the physics ideas the class was considering.
Consistent with the portrayal of dialog in Martin's classroom based upon the rewording instances, almost all of the negative flexible instantiations in his classroom occurred as part of sequences in which Martin attempted to elicit responses to his questions. Some of these sequences included rewording and some did not.
A lack of clarity about Martin's question may have made it difficult for students to respond. However, rather than rewording his question to engage students with the requirements for his original statement (“the closer the object, the smaller F is …”), Martin answered his own question. In another not rewording instance, he appeared to give up, moving on to another topic without answering the question or eliciting an answer from students.No … Your eyes do it automatically. Right? But sometimes in the morning when I just get out of bed and sit there with a cup of coffee and want to read the newspaper, my eyelids droop down. Right? And I cannot get the paper in focus. Anyway, that is that. Well? I have blurred vision. The kind … people say looks to eternity. Do you know what I mean? … So, the pre-requisite is always that the image on the retina is focused at that moment. Right? But then we always assume that.
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Martin: … the goal in introducing the cheat sheet. In the end you want to see the letters as big as possible. Yes? … When do we see them especially big, when do we see them small? It is just about the easiest point. S24, come.
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S24: [No response].
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Martin: Look … S6, come, look.
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S6: What?
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Martin: Once again, the goal of your cheat sheet is – yes? You bring it close that the letters are as big as possible, that you can read it. Right? So when are the letters, when can I see them especially big?
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S6: Yes, when it is close.
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Martin: Yes.
In addition, there were two missed opportunity instances identified in Martin's classroom. In both instances, Martin did not seem to understand the point that the student was making. For example, one instance occurred when Martin's class was discussing how the “eye [is] structured when viewed from a physics perspective,” which entailed identifying different optical components in a drawing of the eye. A student suggested that another lens would be needed because “otherwise it [the image] is the wrong way around.” The student correctly identified that the image projected onto our retinas is upside down; our brains manipulate this image so that a second lens is not required. However, Martin did not seem to recognize that the student had raised a valid point; he responded, “Ah! But think again, the eye. Do we have two lenses?” Relatedly, in the five wording instances in Martin's classroom, he did not seem to recognize the physics content behind students' contributions as he sought particular responses to his questions.
Overall, examination of the flexible instances provides a picture of dialog in the two classrooms. In Peter's classroom, the discussion occurred fairly seamlessly. When glitches such as an unconventionally worded student contribution or a confusingly worded teacher question occurred, Peter was able to keep the conversation on track. He recognized what students were trying to say and helped them to phrase their contributions using the language of physics. He was able to reword his own questions to make them clearer to students. Although he seemed to convey to students that physics ideas should be expressed in only one way, he was able to look beyond students' everyday language to recognize the underlying ideas they were expressing. In Martin's classroom, discussion occurred much less fluently, with frequent misunderstandings and confusion. Martin had difficulty recognizing students' contributions and connecting them to the physics content. His students had difficulty understanding his questions and answering them appropriately. When his questions were not answered correctly, Martin struggled to reword them or to provide appropriate scaffolding. This resulted in extended exchanges in which Martin's students struggled to provide acceptable answers to his questions, often seeming to guess as to what he might be looking for, rather than deeply engaging with the content of the lesson.
Rich Use of Content
Both teachers' lessons focused upon real life examples (overhead projectors, magnifying glasses, and telescopes) and involved multiple representations of optics ideas (ray diagrams, formulas, hands-on investigations). In addition, both teachers made connections to other content (e.g., referring to biology in discussions of the optical properties of the human eye, comparing characteristics of new and previously studied optical components). The proportion of these types of connections was similar across the two classrooms. For both Peter and Martin, twice as many connections involved real life examples (70%) as compared to representations of optics ideas (35%).3 In both classrooms, approximately 10% of the rich instances were connections to other content.
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Peter: Does anyone know how these completely different structures … still [have] the same effect?
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S15: Well, perhaps because of the circles that have various radiuses and then [they can] refract the light differently. Because in the middle there are very small [circles]. And they get bigger and bigger moving to the edge.
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Peter: Yes, you have got the right idea. Ah, that was an important keyword: refraction. Refraction is in the end responsible that the beams of light are deflected when they pass through such a lens. Well, and where is the ray of light refracted?
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[Peter then guides the students to identify how light is refracted in the two lenses.]
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Peter: So the ray of light is only deflected on the surface. The middle area of the convex lens … is not at all involved. And that is the idea behind the Fresnel lens.
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Martin: What happens with the parallel ray then? Perhaps we can help him [the student at the board]. Ah, the parallel ray reaches the first lens, right? And hits the lens. What happens to the ray?
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S24: It is refracted.
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[S24 draws a refracted ray on the diagram on the board.]
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Martin: That means … the glasses lens, that I put in front of [the eye], already refracts the light a little bit. Right? Otherwise, it would arrive completely parallel.
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[S24 returns to his seat and Martin reminds students “we jointly worked out the law of refraction.”]
Fifty-nine percent of the rich instances in Peter's class were deep, with the potential to support students' understanding of the physics content (level 2 on the rubric in Supp. Info. Table 4). The remaining 41% of the coded instances in his classroom included connections that, although not as deep, were strongly related to relevant content (level 1 on the rubric in Supp. Info. Table 4). Looking across Peter's instruction, rich instances occurred in groups, often building from lower to higher level connections (as shown in an earlier example, in which Peter first asked about an optical device containing a convex lens and then asked students to consider how a convex lens functions within a particular device). None of the rich instances identified in Peter's classroom were coded as superficial or unclear (level 0 on the rubric in Supp. Info. Table 4).
In Martin's classroom, over one-third of the rich instances were superficial (27%) or unclear (10%). While these instances suggested connections to the real world or connections between representations, the details of these connections were not made explicit. For example, after Martin's students determined that a second lens (in addition to the eye's natural lens) may be used to magnify an image, he said, “I can remember my great grandmother well. Really. She really had such a fantastic magnifying glass. Yes? And she used it to read her dime novels. She didn't have glasses. She had a real thick magnifying glass.” While this instance includes a real-life example, it is only loosely related to the targeted content and, thus, seems unlikely to support students' understanding of that content (the functioning of a convex lens). Only 15% of the connections in Martin's classroom were judged to be deep and to have the potential to support students' understanding of the physics content (level 2 on the rubric in Supp. Info. Table 4). The remaining connections seemed to represent missed opportunities, such as in the example above, in which Martin referred to the law of refraction but did not discuss how this concept relates to the eye. Although the rich instances in Martin's classroom also occurred in groups, these were less extensive and did not exhibit the same strong pattern of growth in quality that was apparent in Peter's classroom.
Overall, examination of the rich instances provides a picture of how students' understanding of content was supported in the two classrooms. In Peter's classroom, real life examples were brought in and discussed in detail. The deep connections that students were asked to make between these examples and the functioning of the optical components they were studying had the potential to deepen their optics knowledge. Measurements, symbolic equations, and ray diagrams were all used as the class discussed the real life examples; connections among various representations were explicitly addressed, which could deepen students' understanding of both the representations and the relevant physics content. In Martin's classroom, real life examples served as “hooks,” generating interest and connecting physics content to the real world in playful, but not substantive ways. Although multiple representations were also used in Martin's classroom, connections between them were less explicit. Students were often asked to express their ideas using a different representation (as if there were more and less desirable representations) but did not seem to be supported in doing so.
Learner-Centered Use of Content
The lessons provided glimpses of the learner-centeredness of the two teachers' use of content. There were two positive instances in Peter's classroom, in which he explicitly recognized the difficulty that students might experience with particular ideas. For example, as students were identifying the optical components inside overhead projectors, Peter explained to one group that they could ignore one of the components, saying, “It would be too complicated if we were to include that as well … It [the overhead projector] functions … even without this lens. It is only—ah—to compensate for imaging mistakes. To make the colors clearer.” Peter demonstrated an understanding of the components that—given their current levels of understanding—students are equipped to understand and which are crucial for understanding how the overhead projector works.
In contrast, there were two negative instances in which Martin posed a task to his class, only later to determine that they were lacking important prerequisite knowledge. For example, Martin asked his students to complete a worksheet entailing “exactly the representation you saw on the board.” He told them that they “[would] need 4–5 minutes at the most” and that they should complete the task independently. However, after several minutes, it became apparent that the students were unable to complete the worksheet, and a student identified the source of their difficulty: The focal distances were missing. At this point, Martin appeared to recognize that students had not yet learned how to solve problems without this information and made the decision to work through the assigned problems as a class in order to show students how to handle this new type of problem. Although Martin was able to recover from his mistake, he did not predict that students would find the task to be difficult because he did not seem to recognize the prerequisite knowledge it required.
Although further evidence would be required to characterize this aspect of each teachers' PCK, these examples provides some evidence that Peter was more aware of how his students might interact with the content he was teaching them. His instruction was sequenced so that students encountered ideas in a logical manner. In contrast, Martin's students seemed frustrated when asked to solve a problem characterized as straightforward but that they did not have the background knowledge to approach.
Discussion
Limitations
The findings of this study should, of course, be interpreted with caution, as they represent analysis of only two teachers' instruction and only about 90 minutes of instruction per teacher. We certainly cannot make causal inferences about the relationship between PCK and student outcomes, even for these two teachers. The mechanisms posited above are speculations based upon our evidence. In addition, three significant limitations of this study deserve further consideration.
Inferring Knowledge From Teachers' Behavior
As discussed above, this study focused on evidence of teachers' knowledge available through their classroom practice. One concern with this approach is that, while PCK may be recognizable in how a particular topic is taught (Loughran et al., 2001; van Driel, de Jong, & Verloop, 2004), observing classroom events cannot provide a complete portrayal of PCK. Thus, as noted above, we do not claim to capture all aspects of teachers' PCK, and we acknowledge that the learner-centeredness of teachers' use of content is likely to be better represented in other sources of evidence (such as interviews).
A more serious concern has to do with inferring teachers' knowledge from their behavior. While we focused only on the aspect of PCK that seemed most accessible through classroom interactions, we acknowledge that these interactions are influenced by a myriad of factors, and what may appear to be a lack of knowledge could actually represent a reasoned decision to prioritize other factors that remain invisible to the observer (Kennedy, 2010). As Baxter and Lederman (1999) point out, observing the example a teacher chooses to share with his students misses the rationale for that choice, as well as the other examples the teacher decided were not instructionally appropriate. It is, thus, important to emphasize that instead of characterizing what Martin and Peter know, we attempted to explore how their knowledge played out in interactions with students.
Differences Between the Two Classrooms
As noted above, we were not able to identify classrooms that were perfectly matched on all relevant variables. In particular, there were significant differences in terms of two variables that could reasonably be expected to influence teachers' instruction and student responses to that instruction: gender and cognitive ability.
The majority of students in Peter's class were male, while the majority of students in Martin's class were female. Martin's teaching style may reflect efforts to engage a population (female students) that is traditionally underrepresented in physics. However, there is no evidence that girls were particularly advantaged by being in Martin's classroom. The overall patterns of knowledge and interest development from pre-test to post-test for both genders are consistent across the two classrooms. In addition, while Martin's female students may have influenced his choice of examples, it is not clear why they would discourage him from using these examples to make connections to the physics content.
Overall, students in Peter's class had a higher cognitive ability than did students in Martin's class. Martin's struggles to engage students in discussion of physics content, as well as his overall teaching style, may have been influenced by his students' cognitive levels. However, we also believe that some aspects of our evidence cannot be explained in this way. For example, many of Martin's questions seemed incomprehensible; one might actually expect clearer questions to be asked of students with lower cognitive ability.
In addition, personality differences between the two teachers may explain some of the differences we noted. Data from the IPN Video S provides some information about teachers' approaches to instruction but none at the level of detail that would begin to allow us to explore these effects.
Finally, while the two classrooms were matched quite closely in terms of the topic and structure of the lesson, the focus of students' work was not identical. While students in both classrooms were engaged in hands-on work with optical components, the work in Martin's classroom may have appeared more abstract to students. This difference may have influenced students' knowledge and interest, as well as the teachers' instruction.
Lack of Data to Explain Differences Between Classrooms
Because the IPN Video Study focused on characterizing German physics instruction—rather than on explaining how teachers came to teach in particular ways—we have limited information that might help to explain the differences we observed between the two classrooms. In particular, while we might speculate that Peter's extra hours of professional development coursework may have contributed to his use of content in interactions with students, we have no way of testing this hypothesis or of gleaning information about what features of his professional development might be useful for other teachers.
Contributions of the Study
Despite these limitations, this article makes a number of contributions to our understanding of PCK, a construct that is thought to have great importance in teaching and learning.
Contributions to Efforts to Capture PCK
This study describes an approach to capturing one aspect of PCK through video analysis. There are certainly many aspects of PCK that cannot be explored in this way, as well as limitations due to the inferences that are required. However, this approach does not require teachers to articulate what may be tacit knowledge. In addition, exploring teachers' PCK with respect to their own classroom instruction preserves the context-specific nature of this knowledge. Therefore, this approach may offer an important complement to other efforts to capture teachers' PCK.
Perhaps most importantly, like Shulman (1987), we argue that PCK matters most in how it is used. Therefore, while efforts to capture PCK through methods such as paper-and-pencil assessments and interviews are undoubtedly important, we see great value in attempting to capture PCK as it is used in classroom settings. Knowledge that teachers hold but do not use in their practice (e.g., planning, interacting with students) is unlikely to affect the development of students' knowledge and interest. Our focus on PCK-in-action affords two contributions to existing literature. First, we are able to identify how the components of PCK identified by other researchers may play out in interactions with students. This may help to elaborate these components and, thus, make them easier to capture (whether through observations or other assessment approaches). Second, we are able to expand upon these components of PCK, to highlight aspects that may be missed when considering PCK out of the context of its classroom use. In particular, the flexible instances we identified seem to point to the importance of a more spontaneous form of PCK, one extends beyond static knowledge of typical student understandings to more flexible and adaptive knowledge that allows teachers to listen and respond to specific ideas from their own students. While others (e.g., van Driel et al., 1998) have acknowledged the importance of teachers' using components of PCK in a “flexible manner” (p. 675), this study describes what this flexibility might entail in practice. In order to illustrate these two points, we return to the components of PCK identified by van Driel et al. (1998)—knowledge of student learning difficulties and knowledge of instructional representations—and consider how each aspect of teachers' use of content explored in this study elaborates upon and extends existing ideas about PCK.
Teachers' flexible use of content is connected to the first standard component of PCK (knowledge of student learning difficulties) and to Park and Oliver's (2008) inclusion of knowledge of students' “diversity in ability, learning style, interest, developmental level, and need” (p. 266). Rewording—particularly when content-based scaffolding is provided—may require teachers to understand what is difficult about the content they are teaching and to tailor their responses to the particular students in their classrooms. However, recognizing may point to a more spontaneous type of PCK. While recognizing may be aided by knowledge of common difficulties or a repertoire of ways students might express content ideas, these instances require the ability to respond to a range of student ideas and expressions of those ideas, not just ones that can be predicted in advance. Thus the recognizing instances may point to a different type of knowledge: knowledge that allows teachers to make connections between physics content and the ideas their students are expressing (often not articulately and not using scientific language). This is consistent with Fernández-Balboa and Stiehl (1995), who argued that “PCK is not a fixed body of knowledge but instead an ability that enables [teachers] to recognize environmental, personal, and instructional patterns both quickly and accurately” (p. 294). However, our study focuses on teachers' recognition of individual students' content-related ideas, rather than the larger patterns and more generic aspects of PCK considered by Fernández-Balboa and Stiehl.
Teachers' rich use of content is connected to the second standard component of PCK (knowledge of instructional representations). In order to provide real-life examples, teachers must have a set of these examples that they can draw upon during instruction. However, our results point to a more nuanced picture of this component. Rather than simply having a repertoire of instructional representations, our data suggests that teachers must also be able to make connections between various instructional representations and the content they can help to illuminate. This knowledge goes beyond awareness of what examples can be used to illustrate particular content ideas; the explanations that teachers provide surrounding their instructional representations may be just as important as the examples themselves.
Finally, the learner-centeredness of teachers' use of content relates to both standard components of PCK and, again, suggests an expansion beyond current conceptualizations of these components. In particular, this characteristic indicates an interplay between the two components of PCK, such that knowledge of student learning difficulties may inform the sequencing of instructional representations. This is consistent with others who have commented on the intertwined nature of the components of PCK (e.g., Marks, 1990; Park & Chen, 2012; van Driel et al., 1998) and extends these ideas by providing a concrete illustration of how a connection between components of PCK may play out in teacher-student interactions about content.
Contributions to Efforts to Link Teachers' PCK and Student Outcomes
This study provides preliminary evidence for the means by which one aspect of PCK may influence students' achievement and motivation. In this study, there were clear and important differences in how the two teachers used content knowledge in their classroom interactions with students. These differences corresponded to differences in the gains in students' knowledge and interest in a particular domain of physics. This study offers an important contrast to the few studies that have attempted to link teachers' PCK and student outcomes. Previous studies (Kanter & Konstantopoulos, 2010; Roth et al., 2011) assessed teachers' PCK through tasks with some distance from classroom practice: analyzing videos of others' classroom practice and reflecting on videos of their own practice. In order to perform statistical analyses, both studies converted teachers' performance on these tasks into numerical scores—evaluating the quality of teachers' comments on particular types of episodes (Kanter & Konstantopoulos, 2010) or of their teaching strategies (Roth et al., 2011). The study reported in this article permits a richer, qualitative picture of teachers' PCK as enacted in the classroom4 and allows us to begin to provide reasoned speculations about how PCK may actually influence student achievement and motivation—not simply that it does. This may provide an initial foundation for more detailed work to identify the aspects of PCK that are most important for influencing student outcomes.
Contributions to Efforts to Support the Development of Teachers' PCK
- (1)
Gain familiarity with different ways of expressing content ideas so that they can both use and recognize alternatives in the classroom (flexible);
- (2)
develop a flexible understanding of content and the ability to identify content ideas as expressed by novices (flexible);
- (3)
develop a repertoire of examples that can be used to illustrate content ideas and the ability to make explicit connections between different representations of content (e.g., equations, diagrams, graphs) and between examples and content ideas (rich); and
- (4)
learn about common difficulties that students experience with content and consider affordances and constraints of different sequences of content ideas (learner-centered).
The IPN Video Study was part of the priority program BiQua, funded by the German Research Foundation (PR 473/2-2). Funding for the analysis reported in this article was provided by the University of Iowa through an Old Gold Summer Fellowship and International Travel Support from the Department of Teaching and Learning, the College of Education, International Programs, Stanley-UI Support Organization, and the Office of the Vice President for Research.
Notes
1Hill et al. (2008) focused on measurement of a subset of PCK that they call “knowledge of content and students” (p. 373).
2Pseudonyms have been used for both teachers described in this article.
3The percentages do not sum to 100% because instances could be identified as involving multiple types of connections. For example, Martin created a typical ray diagram representing the human eye. Students were asked to identify the parts of the eye corresponding to each component of the diagram. Because this instance involved a real life example (the eye), it was counted as a connection to a real life example. Because students were relating the ray diagram to another representation (the real life eye), it was also counted as a connection between representations.
4Although Roth et al. (2011) followed teachers into the classroom after their professional development program, the intent of these classroom observations was to identify the presence of particular teaching strategies (as a link between teachers' PCK and student learning outcomes), rather than to examine teachers' PCK in action.
