Revisiting the origin of,and reflections on the future of,pedagogical content knowledge

Abstract

More than 35 years have passed since Shulman introduced the term “pedagogical content knowledge” [PCK] to the field of teacher education. As is the case with any new construct in a field, Shulman's advocacy for PCK in the mid-1980s was almost certainly a reaction to the priorities of the field at that time. A primary goal of this paper is to refresh our collective memories of the origins of and development of PCK as a research domain, with a particular focus on what may have prompted scholars such as Shulman to propose the construct of PCK in 1986. With this historical lens as background, I also seek to consider what might be fruitful future directions in the field's thinking about teaching and teacher knowledge.

1. Introduction

More than 35 years have passed since Shulman introduced the term “pedagogical content knowledge” [PCK] to the field of teacher education. Almost from the beginning, interest from both the researcher and practitioner communities in PCK has been high, especially among those who study mathematics teaching and learning. At present, the field's belief in the promise and utility of the construct of PCK shows no signs of abating.

As is the case with any new construct in a field, Shulman's advocacy for PCK in the mid-1980s was almost certainly a reaction to the priorities of the field at that time. In other words, Shulman and others who played a key role in the initial work on PCK were intentionally seeking to push the field away from a particular set of research foci (that they perceived did not sufficiently foreground teacher knowledge) and toward a different set of priorities for which the construct of PCK was necessary.

Not surprisingly given the passage of time, our memory of the state of our field in the 1980s has faded. Yet I believe that it is useful for us to keep in mind the initial conditions in which PCK was introduced. By remembering the origin story of PCK and thus situating its introduction within the context of the conditions and arguments that were occurring at the time, we are in a much better position to reflect on the current state of research on PCK and teachers’ knowledge more generally and to think about the most productive directions for future research in this area.

A primary goal of this paper is to refresh our collective memories of the origins of and development of PCK as a research domain, with a particular focus on what may have prompted scholars such as Shulman to propose the construct of PCK in 1986. What were the questions in the field at that time to which Shulman believed that PCK was the answer? With this historical lens as background, I also seek to consider what might be fruitful future directions in the field's thinking about teaching and teacher knowledge.

2. State of affairs in the mid-1980s with respect to mathematics education research

2.1 The introduction of PCK to the field

Shulman introduced the construct of pedagogical content knowledge in his seminal Educational Researcher article from February 1986 (Shulman, 1986). This paper was first presented as Shulman's presidential address at the April 1985 annual meeting of the American Educational Research Association in Chicago. The ideas from the 1985 address/1986 paper were further elaborated in a 1987 paper published in the Harvard Educational Review (Shulman, 1987), a paper that was selected for publication in a November 1986 special issue of that journal on “Teachers, Teaching, and Teacher Education” but was published in February 1987 due to “the exigencies of publishing.” Shulman's ideas about teacher knowledge developed during his time on the faculty of Michigan State University (1963–1981), particularly in the context of his founding of (in 1976) and leadership in Michigan State's Institute for Research on Teaching (Shulman, 2002). This line of work continued when he moved to Stanford University in 1982.

Shulman suggested that it was important to distinguish between three categories of teachers’ content knowledge: subject matter content knowledge, pedagogical content knowledge, and curricular knowledge. He wrote, “A second kind of content knowledge is pedagogical [content] knowledge, which goes beyond knowledge of subject matter per se to the dimension of subject matter knowledge for teaching. I still speak of content knowledge here, but of the particular form of content knowledge that embodies the aspects of content most germane to its teachability” (Shulman, 1986, p. 9). He further described PCK as “the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations—in a word, the ways of representing and formulating the subject that make it comprehensible to others” (Shulman, 1986, p. 9), “an understanding of what makes the learning of specific topics easy or difficult: the conceptions and preconceptions that students of different ages and backgrounds bring with them to the learning of those most frequently taught topics and lessons” (Shulman, 1986, p. 9), and “knowledge of the strategies most likely to be fruitful in reorganizing the understanding of learners” (Shulman, 1986, p. 9–10).

Shulman argued that his ideas about teachers’ knowledge were innovative and pushed the field into productive new territory, in at least two ways. First and foremost, Shulman sought to shift attention from teacher behaviors—which had been a focus of prior scholarship—to teacher knowledge: “From observable performance to strategy and understanding; and from simple models of stimulus and response to more complex and subtle models involving content, context, and cognition” (Shulman, 2002, p. 249–250).

In fact, at that time, the attention of contemporary mathematics education researchers was more generally turning to questions about knowledge. In 1986, Hiebert's seminal edited book “Conceptual and Procedural Knowledge: The Case of Mathematics” (Hiebert, 1986) was published. This book contained chapters written by leading scholars in mathematics education and cognitive psychology that emerged from a seminar series on students’ knowledge of mathematics at the University of Delaware in 1984. This same period was also when Carpenter and colleagues at the University of Wisconsin – Madison were doing research on elementary children's knowledge about arithmetic word problems and advocating instructional methods that incorporated students’ mathematical thinking; this seminal work is generally referred to using the label CGI, or cognitively guided instruction (e.g., Carpenter et al., 1989).

Note that the field at that time was immersed in the study of students’ knowledge of mathematics; Shulman felt that this same attention could be productively used to investigate teachers’ knowledge of mathematics. But he felt that doing so would inevitably require the identification of categories of knowledge that did not currently exist (particularly PCK), given that PCK is a synthesis of, or transformation of, regular content knowledge into content knowledge that is more useful for teachers.

A second aspect of Shulman's work that he felt was innovative was his push for the field to focus its attention on teacher education. Shulman pointed to scholars’ increasing interest in knowledge growth among teachers and felt that there was a pressing need for a strong theoretical framework to guide this work. He noted particularly important and unanswered questions that were central to this effort, including, “What are the domains and categories of content knowledge in the minds of teachers? How, for example, are content knowledge and general pedagogical knowledge related? In which forms are the domains and categories of knowledge represented in the minds of teachers? What are promising ways of enhancing acquisition and development of such knowledge?” (Shulman 1986, p. 9). In anticipating the answers to these questions about knowledge development, Shulman believed that there likely needed to be a new categorization scheme for teachers’ knowledge—and this is where PCK became necessary and useful.

Shulman astutely identified an area of need and interest for the field, and numerous scholars turned their focus relatively quickly toward PCK. In the late 1980s, Shulman directed a series of dissertations at Stanford that explored and elaborated on the construct (e.g., Grossman, 1988; Wilson, 1988; Wineburg, 1990); many of his students went on to do ground-breaking work related to teachers’ knowledge (e.g., Howey & Grossman, 1989; Wilson & Wineburg, 1988). Numerous frameworks for teacher knowledge—including PCK as well as other knowledge categories—were formulated and researched, not only in mathematics education (e.g., Carrillo-Yañez et al., 2018; Hill et al., 2008; Rowland et al., 2005) but also in science education (Carlson et al., 2019) as well as in several other disciplines (e.g., Backman & Barker, 2020; Dyment et al., 2018; Powell, 2018; Yadav & Berges, 2019), both domestically and internationally. Interest in PCK and related constructs continued into the 2000s and 2010s; the US National Science Foundation reported that between 2011 and 2015, 27 projects were funded that were related to PCK, totaling over US$60 million (Miller et al., 2022). Furthermore, the original 1986 and 1987 publications from Shulman continue to be widely cited, with each accumulating more than 30,000 citations to date, more than perhaps any other publications in the field of education.

To summarize the context to which Shulman introduced the idea of PCK, researchers in the 1980s were already very interested in students’ knowledge growth, but investigations of teachers’ knowledge growth were more novel. Shulman (among others) sought to change this. Through his efforts prior to and after 1985, we see the emergence of theoretical and empirical work aimed at identifying the types of knowledge that teachers have—all in parallel to contemporary efforts investigating the types of knowledge that students could develop. As part of this work, Shulman foresaw the need for the identification of new forms of content knowledge to describe the knowledge implicated in teaching or PCK. Shulman envisioned PCK as a synthesis of, or transformation of, “regular” content knowledge into content knowledge that is more useful for teachers.

2.2 The field's prior focus on teacher behaviors

As noted above, Shulman expressed his view that the field of education—particularly with respect to the study of teaching—had been dominated by a focus on teacher behavior. Shulman notes, “In reading the literature of research on teaching, it is clear that central questions are unasked. The emphasis is on how teachers manage their classrooms, organize activities, allocate time and turns, structure assignments, ascribe praise and blame, formulate the levels of their questions, plan lessons, and judge general student understanding. What we miss are questions about the content of the lessons taught, the questions asked, and the explanations offered” (Shulman, 1986, p. 8). He also writes about “… a growing body of research on teaching, research classified under the rubrics of ‘teaching effectiveness,’ ‘process-product studies,’ or ‘teacher behavior’ research. These studies were designed to identify those patterns of teacher behavior that accounted for improved academic performance among pupils” (Shulman, 1986, p. 6). Here, Shulman is referring to a well-established line of research in education that many refer to as “process-product” studies, as this work was centrally about the search for relationships between classroom processes (e.g., teaching) and classroom products (e.g., what students learn). This type of research was the norm in education—especially in teacher education—in the United States from about the late 1950s to the mid-1980s.

As a window in the process-product research paradigm, we can look to a chapter by two prominent scholars who did work in this tradition, Jere Brophy and Thomas Good, that appeared in the 1986 Handbook of Research on Teaching (Brophy & Good, 1986). This chapter reviews the corpus of process-product studies about teaching that had been conducted in the past decade. Approximately 200 studies are discussed in this chapter, addressing a very wide range of topics related to teachers and teaching. Brophy and Good discuss clusters of research related to students’ opportunity to learn, teacher expectations, teachers’ use of time in the classroom, classroom management, active group instruction, optimal modes for teachers’ presentation of information, teacher question asking, teacher feedback to students, assignment of and use of homework, and many other topics. This chapter makes a convincing case that investigations of teaching—within the process-product tradition—were quite numerous in the field at this time, resulting in a substantial scholarly knowledge base about the teaching and learning process.

In general, there were two main types of studies within the process-product research paradigm. The first type of study explored correlations between observed classroom features and students’ achievement. In these types of studies, classrooms were naturalistically observed using an observation system (of which there appear to have been hundreds in use at that time), and the frequency of various features of the observed teaching were correlated with students’ achievement on standardized assessment measures. The second type of study was experimental studies. In these studies, teachers were trained to implement particular features of teaching (features that often emerged from the first type of studies mentioned above) that had been found to be positively linked to higher student achievement. Subsequently, these teachers were observed to monitor whether they used these features with the desired quality and frequency and whether students’ learning improved as a result.

As one prominent example within the context of mathematics teaching, consider a study by Thomas Good (the author of the handbook chapter mentioned above) and (Good & Grouws, 1979; see also Ebmeier & Good, 1979) that exemplified the second type of study but is informed by a prior program of research over approximately a decade that included many studies of the first type. This program of research began with a large correlational study, where Good and colleagues collected 3rd, 4th, and 5th-grade students’ scores on a commonly used standardized test, the Iowa Test of Basic Skills, in 1972, 1973, and 1974, from over one hundred classrooms; these data served as the “product.” At the same time, trained observers visited the classrooms of all participating teachers while math was being taught. Each teacher was observed for 5–7 lessons. In each class session, while observing, trained raters completed very detailed observation instruments that tracked both low inference items such as teachers’ actions, words, and use of time, as well as higher inference items such as classroom climate, classroom organization, clarity of instruction, student attention, teacher and student enthusiasm, and more. These data served as the “process.” The subsequent analyses correlated all process variables with the standardized test results, resulting in the identification of numerous aspects of teachers’ instruction that was highly correlated with students’ achievement scores.

From these correlational relationships, Good and colleagues then formulated a set of key instructional behaviors that were hypothesized to be linked to higher student achievement. In this particular study, these instructional behaviors included an 8-min daily review (during the first minutes of each class period except for Mondays), about 20 min of “development” (focusing briefly on prerequisite skills and concepts but followed by a focus on “meaning and promoting student understanding by using lively explanations, demonstrations, explanations, illustrations, etc.”; Good & Grouws, 1979, p. 357), and 15 min of seatwork.

Subsequently, the effectiveness of this set of key instructional behaviors was experimentally evaluated. Forty fourth- and fifth-grade teachers were randomly assigned to a treatment or a control group, and treatment teachers were trained in the instructional program described above. Teachers were observed by trained raters to determine the extent that they were implementing all features of the instructional program, and the researchers determined whether the students of treatment teachers—particularly those teachers who faithfully implemented the instructional program—scored higher on standardized assessment outcomes than students of control teachers. Good and colleagues (Ebmeier & Good, 1979; Good & Grouws, 1979) found here that students in treatment teachers’ classrooms did indeed score significantly higher than students in control teachers’ classrooms. The authors conclude by noting, “[This study] is part of a recent trend in research on teaching that is beginning to show that not only do well-designed process-outcome studies yield coherent and replicable findings, but treatment studies based on them are capable of yielding improvements in student learning that are practically as well as statistically significant. Such data are an important contradiction to the frequently expressed attitudes that teaching is too complex to be approached scientifically and/or that brief, inexpensive treatments cannot hope to bring about significant results” (Good & Grouws, 1979, p. 361).

2.3 Debates about the value of the process-product research paradigm

Although it was the predominant lens for research on the effectiveness of teaching from the 1960s to the 1980s, the process-product paradigm was not without its detractors. Concerns about this mode of research appeared to reach a crescendo in the 1980s, when debates in the field on the merits of (and concerns about) process-product research appeared regularly in prominent educational research journals and handbook chapters (e.g., Erickson, 1986; Gage & Needels, 1989; Garrison & Macmillan, 1984; Macmillan & Garrison, 1984; Phillips, 1981; Tom, 1980). In the mathematics education community, criticism about process-product research paralleled the rise in interest in students’ mathematical thinking, as mentioned earlier (e.g., Carpenter et al., 1989). In particular, and in another chapter in the abovementioned 1986 Handbook of Research on Teaching, prominent mathematics education researchers Romberg and Carpenter highlighted some of the field's most pressing issues with process-product research (Romberg & Carpenter, 1986). Their concerns focused on (a) the use of standardized tests as outcome measures in these studies, (b) the lack of a theoretical explanation to accompany correlations between certain teacher behaviors and student outcomes (e.g., the inductive approach on which the process-product paradigm is based), (c) the reliance on quantity vs. quality in identifying important features of classroom instruction (e.g., they write, “Who is to say that a large number of questions posed by the teacher is more potent than a single question raised at the ‘right’ moment in an instructional episode?” (p. 861), (d) the generic, global nature of teaching recommendations, with no grounding in the mathematical content, and (e) the apparent link between the recommended teacher behaviors and a specific (traditional, direct instructional) mode of teaching. They conclude, “In general, the ‘scientific’ studies related to the teaching of mathematics have failed to provide teachers with a list of tested behaviors that will make them competent teachers and ensure that their students will learn” (p. 865).

In response to these critiques, it is instructive to look at a 1986 article in the Journal for Research in Mathematics Education [JRME] by Jere Brophy, an educational psychologist and leading voice in the process-product research tradition (and the process-product handbook chapter author noted above). Brophy was invited by JRME to write about “how content might be taught and skills might be developed in typical elementary and secondary classrooms” (Brophy, 1986, p. 323) and to suggest lines of research for the field related to math instruction.

Brophy took this opportunity to respond to some of the criticisms of process-product research that had been raised by mathematics educators, including those from Romberg and Carpenter (1986) as noted above. Brophy writes, “my belief [is] that many mathematics educators have a limited and distorted view of the existing research on classroom teaching” (p. 323). In particular, Brophy characterizes Romberg and Carpenter's (1986) handbook chapter as reviewing “(mostly naturalistic) research on children's development of cognitive and metacognitive skills and mathematics concepts. … In covering the research on teaching, however, the authors’ emphasis is on a criticism of the conceptualization, design, and methodology of the research rather than on coverage of its substantive findings. It is not much of an exaggeration to characterize the first half of the chapter as, ‘What research on children's development and learning has to offer mathematics educators’ and the second half as ‘Why mathematics educators should be wary of research on teaching.’ Comparisons of this chapter with the chapter by Brophy and Good (1986) in the same handbook on research linking teacher behavior to student achievement give the impression that the two sets of authors live in different worlds” (p. 323–324).

Brophy goes on to elaborate on his perception of the wide chasm between the ways that the field of education was thinking about research on teaching (via the process-product paradigm) and how mathematics education researchers approached this topic (from the perspective of student thinking and cognition). In particular, Brophy criticizes mathematics education researchers for having an overly narrow view of research on teaching and urges them to broaden their perspective, in three ways. First, Brophy characterizes mathematics education research at the time as mostly focusing on curriculum and not addressing teaching practices. Brophy acknowledges the importance of knowing about cognition when designing curricula. But he expresses his belief that “it is also important to recognize that schools are established to ensure that students acquire certain knowledge and skills, especially cognitive knowledge and skills that would be acquired only partially and haphazardly without systematic instruction” (p. 324). Brophy pushes mathematics education researchers to do more research on “what to teach children and how to teach it effectively” (p. 325); he claims that mathematics education researchers need to shift their thinking to focus more on instruction, not merely on curriculum and learning.

Second, Brophy makes a particularly strong claim about modes of instruction that he favors (and that he perceives the research base supports) for mathematics learning. He writes, “Mathematics educators need to think more about proactive, direct instruction linked to prescribed objectives. Even when they do speak of instruction, mathematics educators tend to describe what might be characterized as reactive tutorial assistance, provided during one-to-one interactions conducted at a leisurely pace in a private setting, designed to stimulate discovery learning by a bright, well-motivated learner” (p. 325). Brophy raises concerns about the feasibility of “individually guided discovery” (p. 325) as a form of mathematics instruction—a form of instruction that he believes is preferred by mathematics education researchers. Third and related, Brophy argues that traditional forms of mathematics instruction (which he characterizes as direct instruction by the teacher, in contrast to a more individualized, inquiry-oriented tutorial pedagogy) are a practical necessity for effectively improving students’ learning of mathematics. Brophy writes, “The traditional whole class instruction recitation seatwork method is the simplest to manage, and it enables the teacher to continuously instruct the students or supervise their work on assignments” (p. 326).

In concluding his critique of mathematics education research, Brophy provocatively writes, “In combination, these considerations appear to leave mathematics educators with two choices: either grumble about the imperfections of schooling as we know it and await a miracle or stop dreaming of Utopia and work to make the best of the situation by developing systematic approaches to curriculum and instruction that are designed to be implemented within the constraints that apply in the typical classroom setting” (p. 326).

The above-noted criticisms of process-product research from Romberg and Carpenter (1986) and the subsequent responses from Brophy (1986) encapsulate much about the context of the mid-1980s in the United States when Shulman introduced the concept of PCK. We see the existence of an extensive, robust, and very detailed research base from educational psychologists on instruction and features of good instruction, largely from the process-product literature. At the same time, there is a growing perception that such a research base is not sufficiently grounded in content, context, and contemporary theories about learning (e.g., constructivism) and teaching. There is also an extensive and growing research base on student knowledge development in mathematics that Shulman seeks to expand to teacher knowledge, requiring the introduction of a new form of knowledge that he calls PCK.

3. Implications for current and future research on PCK in mathematics education

With the above as a reminder of the historical and contextual factors in mathematics education research in the United States in the 1980s at the time that PCK was introduced, I turn now to some personal reflections on research on PCK and related constructs in the present day. I begin by noting that Shulman's apparent goal when introducing PCK—turning the field toward consideration of teachers’ knowledge—has largely been achieved. The past 30 years have seen a remarkable shift in the ways that we think about teaching and teachers’ knowledge. The theoretical and empirical work around PCK has arguably had a significant and influential impact on research, policy, and practice. However, at the same time, I found that this historical reminder of the origin story of PCK raised interesting and challenging issues for me, several of which I discuss below. In general, I wrestle with how the passage of time—from 1986 to the present, and from the present to 35 years in the future—might change our ideas about and research about PCK and teachers’ knowledge.

3.1 Implicit links between PCK and preferred forms of instruction

First, I had not previously been aware of the clear but often implicit links between PCK and a particular view of pedagogy—namely, inquiry-oriented, student-centered, reform, and constructivist teaching of mathematics. I note that PCK became popular in mathematics education research at precisely the same time that the field became convinced of the merits of constructivist teaching, as instantiated in the original 1989 NCTM Standards. As noted above, in the 1980s, mathematics educators made a strong case that mathematics teaching, and mathematics teachers, should foreground student thinking. This vision of mathematics instruction emphasizes the critical importance of teachers’ eliciting, noticing, and acting upon students’ reasoning, conjectures, ideas, and strategies. As a result, teachers who teach in a constructivist manner need very sophisticated knowledge of student thinking, including knowledge of possible student strategies and alternative forms of representation that students might use; this knowledge lies at the very heart of PCK. In hindsight, it is no coincidence that the trajectories of interest in PCK and in constructivist teaching follow a similar arc, with a huge surge beginning in the 1980s and continuing to the present.

Ironically, recall that mathematics education researchers critiqued the process-product research paradigm for being too linked to a (different) model of instruction—namely, so-called traditional instruction (as characterized by Romberg and Carpenter, 1986), which fell out of favor beginning in the 1980s. The process-product paradigm's link to traditional instruction contributed to its demise, in much the same way that PCK's link to constructivist teaching enhanced its appeal. A skeptic might notice that present-day scholars do not seem concerned that their preferred research paradigm (related to studying teachers’ knowledge and PCK) is tightly linked to their preferred form of instruction (constructivist), but their intellectual ancestors complained quite loudly when a different research paradigm (process-product) was tightly linked to another, less preferred form of instruction (traditional). From its introduction, it appears that the construct of PCK has not been neutral in the field's battles over preferred forms of instruction but instead is tightly linked to constructivism as a preferred mode of teaching.

When this implicit link between the construct of PCK and constructivist forms of instruction is unveiled, there are several difficult questions about PCK that one might pose—questions that get at the heart of the meaning and utility of this construct. For example, one could reasonably ask whether robust PCK is necessary—or as necessary—if a teacher does not utilize student-centered pedagogies. Is PCK essential for teachers to have, regardless of how they teach? Similarly, as our ideas about what constitutes good instruction shift (as they inevitably do), does this change what we hope teachers know in terms of PCK? Imagine that the educational climate of the future shifts such that direct (traditional) forms of instruction became the recommended and dominant form of pedagogy. What knowledge would teachers need to become excellent practitioners of direct instruction, and would this knowledge align with current conceptions of PCK? Might PCK become obsolete in the future if constructivist pedagogies go out of favor? Is there a need for specialized content knowledge for teaching in a direct instructional teaching environment, where attending to student thinking is not a high priority? Present-day researchers appear to operate on the assumption that PCK is a critical and universal need for teachers. But how confident are we in the validity of this assumption, given the implicit and often unacknowledged link between PCK and constructivist forms of instruction?

3.2 Developmental transformation of PCK to CK

The passage of time—with the inevitability of changing perspectives about the most effective ways to teach mathematics—raised some difficult questions for me in terms of PCK and related constructs. It might also be the case that the passage of time forces us to confront shifts in what knowledge is PCK at all. Might it be the case that knowledge that we currently call PCK is, in the future, not PCK at all but is “mere” content knowledge? At present, PCK is conceived of as specialized knowledge of mathematics that teachers need but that students do not need. But what if in the future we expect students to learn the same content that we presently think that only teachers need to know? If this occurred, knowledge that we currently call PCK—specialized knowledge needed only by teachers—might in the future merely be content knowledge—or knowledge that we expect teachers and students to know as a normal part of the mathematics curriculum.

Arguably, this phenomenon has already occurred. Consider our present interest in multiple representations of functions in the algebra curriculum. In a shift that can be traced at least back to the 1980s (perhaps as part of the field's larger interest in student thinking at that time), mathematics educators were and are quite interested in teaching multiple representations of functions during algebra learning. In the present day, students are expected not only to know how to work with symbols when learning about functions and equations but also to become fluent in using tables and graphs. Understanding connections between multiple representations of functions is a core component of what it means to develop robust knowledge of algebra.

Yet prior to the 1980s, only teachers would have been expected to have sophisticated knowledge about the use of tables and graphs for representing functions. In these “old” days, teachers might have been expected to leverage their knowledge of tabular and graphical representations to support student learning, given that using tables and graphs constituted “the ways of representing and formulating the subject that make it comprehensible to others” (Shulman, 1986, p. 9)—in other words, PCK. This was not knowledge that students were expected to know at that time, but certainly it was useful for teachers to know. Thus, knowledge of how to use tabular and graphical representations of functions could be considered pre-1980s-PCK that is now present-day CK, or part of the knowledge that everyone, including students and teachers, is expected to learn in the algebra curriculum. As the field's ideas about student learning goals and curriculum shift, what we once considered to be PCK could become “mere” content knowledge—or even disappear completely from consideration.

In fact, one could wonder whether the entire construct of PCK might be transmuted into content knowledge at some point in the future, such that PCK ceases to be a useful knowledge category at all; such obsolescence of PCK might even be considered a monumental achievement in mathematics teaching and learning. Consider what might happen if we were able to provide “perfect” instruction to all students, such that they met our most ambitious learning objectives for the learning of mathematics. When these students grew up to be mathematics teachers, what (if anything) would be left in the category of PCK? Would students’ deep, full understanding of the content provide them with all of the (content) knowledge that they needed to successfully teach mathematics, such that PCK was no longer needed? As we become more and more skilled at teaching mathematics (and supporting students’ learning of mathematics), this has the long-term effect of improving our future teachers’ knowledge of mathematics. Does this in turn result in the reduction and gradual elimination of the need for, and thus the construct of, PCK for teachers?

3.3 Moving from knowledge back to behavior?

As this examination of the history behind PCK's introduction makes clear, starting in the 1980s the field moved from a predominant focus on teacher behaviors (in the process-product research paradigm) to the present focus on teacher knowledge. Many have framed this shift from the lens of behaviors to the lens of knowledge as a significant advance in the ways that we conceive of and investigate teaching and teacher preparation. With the passage of time, one wonders whether a future day might arrive when the field moves away from knowledge and back to a central focus on behaviors. If the introduction of PCK led researchers to shift from studying teacher behaviors to studying teacher knowledge, perhaps we will one day see the pendulum shift back toward a reconsideration of teacher behaviors and actions as an important means to study and to improve teaching. Arguably, this shift back to foregrounding teacher behavior is already happening, as illustrated by two distinct and emerging areas of research in our field.

3.3.1 Automated, “Big Data” analyses of classroom practices via natural language processing

First, there is growing interest in leveraging the power of “big data” in research on teaching. It is increasingly the case that video records of teaching practice (especially in the United States) are relatively easy to obtain, but only recently have data science tools existed that can perform automated analyses of videotaped teaching via lesson transcripts. Mathematics education researchers have been engaged in careful analyses of video records of teaching since at least the early seminal work of Lampert (1990) and others. Present-day scholars, with the assistance of computational tools, can now do similar but automated analyses on hundreds or thousands of lessons.

For example, Demszky and colleagues began with a database of transcripts of hundreds of 4th- and 5th-grade math lessons (from the Measures of Effective Teaching [MET] project; Kane & Staiger, 2012) and, using natural language processing, were able to computationally identify instances in the lessons where teachers reacted to students’ utterances in productive and generative ways (Demszky et al., 2021) and where teachers utilized instructional practices that were responsive to student thinking (Alic et al., 2022). Similarly, Suresh and colleagues (2022) created a database of transcripts from over 500 math lessons and computationally analyzed teachers’ utterances for the prevalence of “talk moves” within the widely used accountable talk framework (Michaels et al., 2008). Liu and Cohen (2021) did a similar analysis using transcripts of hundreds of English Language Arts lessons and were able to computationally detect the prevalence of teachers’ classroom management strategies, interactive instruction, and teacher-centered instruction. Computational linguists have been conducting automated analyses of transcripts/texts for some time, but only in the past 5 years have we seen collaborations between these scholars and educational researchers. These research teams are now engaged in analyses of classroom lesson transcripts to document the prevalence of particular features of teachers’ behaviors.

Although the full impact of using data science tools to help us understand more about mathematics teaching remains to be seen, this approach does represent a potentially significant shift in how the field conceives indicators of effective teaching. Instead of trying to identify ways to investigate, improve, or assess teachers’ knowledge, natural language processing of classroom lesson transcripts focuses attention on teachers’ behaviors, particularly their utterances. Transcript analyses begin with the same type of naturalistic observations that were at the core of studies conducted in the process-product tradition. Whether one views this line of research as complementary to or a replacement for the PCK lens on studying teaching, it is quite novel.

3.3.2 Practice-based teacher learning opportunities

A second area of research that may indicate a renewed interest in teachers’ behaviors is the use of rehearsals, approximations of practice, teaching simulations, and other practice-based teacher learning opportunities (or “pedagogies of enactment”, Grossman & MacDonald, 2008) for supporting teacher growth. Rather than seeking primarily to develop teachers’ knowledge (with the assumption that improving teacher knowledge will subsequently improve their practice), many teacher education scholars focus more directly on the behaviors or actions of teaching (e.g., Cohen et al., 2020; Kavanagh et al., 2019; Kavanagh et al., 2020). This type of direct intervention in teachers’ practice occurs within the context of carefully curated clinical experiences, with the explicit goal of preparing teachers to teach.

Many trace the origins of this shift from teacher knowledge to practice-based teaching opportunities to seminal work by Grossman and colleagues (Grossman et al., 2009; Grossman & McDonald, 2008); recall that Grossman was a student of Shulman and a prominent early scholar of PCK. Grossman and colleagues urge the field to take seriously the affordances provided by clinical aspects of teaching, particularly as tools for helping novice teachers improve their teaching. They note, “We want to argue that teacher education should move away from a curriculum focused on what teachers need to know to a curriculum organized around core practices, in which knowledge, skill, and professional identity are developed in the process of learning to practice” (Grossman et al., 2009, p. 274).

In mathematics teacher education, practice-based learning opportunities have frequently been used to help teachers develop and improve the ability to facilitate productive mathematical discussions (e.g., Ghousseini & Herbst, 2016; Lampert et al., 2010; Lampert et al., 2013). Although mathematics education researchers may view practice-based learning settings as rich opportunities for teachers to acquire PCK, the focus of research in this area is on the design of and use of the practice-based learning structures themselves. In other words, researchers seem most interested in the direct effects of rehearsals, simulations, etc. on teachers’ instruction, rather than the effect of these practice-based learning opportunities on teachers’ PCK. Something quite different seems to be happening in the field of science teacher education research, where scholars have expanded conceptions of science teachers’ PCK such that both knowledge and behaviors are captured under the same construct (Hume et al., 2019). In particular, the Refined Consensus Model of science teachers’ PCK (Carlson et al., 2019) now includes both traditionally considered (personal) elements of PCK (pPCK; Alonzo et al., 2019) and enacted PCK (ePCK; Alonzo et al., 2019), which they view as pedagogical content knowledge in action.

While acknowledging the important role of teachers’ knowledge in instruction, practice-based teacher learning opportunities appear to represent a shift in the field's focus, moving PCK into the background and instead foregrounding teachers’ actions. It is also worth noting that recent empirical evidence supports the utility of this shift; for example, Gonzalez et al. (2022) found that teachers’ practices seem to have a stronger influence on student learning than does teacher knowledge. With each inevitable swing of the pendulum between a focus on knowledge and a focus on behavior, it may be the case that we improve our ability to conceptualize and investigate the expertise and artistry that are inherent in effective teaching.

4. Concluding thoughts

Shulman's introduction of PCK came at a particular time in US educational research, one characterized by an interest in student cognition, thinking, and knowledge; a move away from certain kinds of experimental, empirical, psychological forms of classroom research (from the process-product tradition); an embrace of constructivist theories of learning; and an interest in thinking deeply about teacher education. PCK pushed the field to move away from thinking about teaching solely in terms of teacher behaviors and instead to consider conceptualizations of and interventions on teacher knowledge.

Given that 35 years have passed since PCK's introduction, one wonders what changes may emerge in the ways that we conceptualize and investigate teaching. If constructivist theories of learning go out of favor, will this (or should this) change how we think about PCK? As ideas shift about the mathematics content that we teach, might this impact the knowledge that we consider to be PCK, as opposed to “mere” content knowledge? And after a productive period of foregrounding teacher knowledge in our work, might we now be seeing a return to foregrounding teachers’ actions and behaviors in our research on teachers and teaching? As researchers interested in effective teaching, it may behoove us to keep in mind the words of Machiavelli, who noted, “Whoever wishes to foresee the future must consult the past; for human events ever resemble those of preceding times.”