Creating Practical Theories of Teaching

Abstract

In this chapter we propose a way to create theories of teaching that are useful for teachers as well as researchers. Key to our proposal is a new model of teaching that treats sustained learning opportunities (SLOs) as a mediating construct that lies between teaching, on the one hand, and learning, on the other. SLOs become the proximal goal of classroom teaching. Rather than making instructional decisions based on desired learning outcomes, teachers could focus on the kinds of SLOs students need. Because learning research has established reliable links between specific types of learning opportunities and specific learning outcomes, theories of teaching no longer must connect teaching directly with learning. Instead, theories of teaching can become theories of creating SLOs linked to the outcomes teachers want their students to achieve. After presenting our rationale for moving from theories of teaching to theories of creating SLOs, we describe the benefits of such theories for researchers and teachers, explain the work needed to build such theories, and describe the conditions under which this work could be conducted. We conclude by peering into the future and acknowledging the challenges researchers would face as they develop these theories.

1 Creating Practical Theories of Teaching

Imagine the challenges faced by Lucy Scott, a sixth-grade teacher planning a unit on equivalent fractions. She is deciding what tasks to use and how to discuss them with her students. Ms. Scott has taught these lessons before and knows she needs to make some changes. The last time she taught the lessons, the students seemed confused, leaving Ms. Scott unsure, at the end, whether or not her students really understood what it meant for fractions to be equivalent. How can Ms. Scott decide what changes to make? Are there theories that could help her predict, for example, what might happen if she chose one task over another? Do such theories even exist?

We begin this chapter with the unusual proposition that it is possible to build theories of teaching—practical theories—that are useful for teachers. At the heart of our argument is the concept of learning opportunities, specifically learning opportunities that can be sustained within and across daily classroom lessons. Rather than assuming that teaching behaviors have a predictable impact on student learning, we argue that it is the sustained learning opportunities (SLOs) created by these behaviors that predict student learning. In order to help students achieve particular learning goals, teachers need to create SLOs aligned with these goals. The creation of these opportunities provides a more proximal goal for teachers than the achievement of learning outcomes. Focusing on SLOs opens the possibility for teachers to reason in cause-effect terms because it is easier to anticipate the effects of teaching behaviors on SLOs than on learning outcomes.

We develop our argument by first discussing a simple model that has often guided research on teaching and its effects on learning. We then describe a more complex model, created to fix the simplistic assumptions of the simpler model. Although both of these models have generated a number of useful theories and programs of research, we claim that theories of teaching effectiveness based on these models have reached their limits for generating research that will take the field beyond where it is now. In addition, we do not believe these models can support theories that teachers can use to make instructional decisions. We argue that a different model is needed to further advance theories of teaching effectiveness and bring them closer to the work of teachers.

Our alternative model inserts a new, single, mediating construct—sustained learning opportunities, or SLOs—between teaching and learning. SLOs can be defined as the temporarily stable systems that emerge during classroom lessons from the interactions of multiple mediating variables to create the contexts in which learning occurs. A SLO is a unit of analysis that provides the pathway through which teaching leads to significant learning. We present our alternative model by elaborating the construct of SLOs, clarifying how the model differs from previous mediating variables models, and examining the essential role this new construct plays in mediating the connections between teaching and learning. Our aim is to present a convincing argument that a theory of teaching most useful for teachers will be a theory that guides the creation of SLOs.

We continue by explaining how our model drives the shift from theories of teaching to theories of creating SLOs, and we lay out the key ingredients of these theories. We present an example of a mini-theory that could be knit together with other mini-theories to create larger theories, and we step back to imagine ways in which teachers and researchers, as well as partnerships they might form, could use the construct of SLOs to build usable theories. We conclude our argument by acknowledging the challenges of developing theories of creating SLOs while still setting this goal as a worthy pursuit.

Kurt Lewin is credited with saying, “there is nothing as practical as a good theory” (Greenwood & Levin, 1998). Although theories of teaching effectiveness have usually been treated as guides for researchers, we interpret Lewin’s phrase as a hypothesis that “good theories” could exist for practitioners as well as researchers. This is not to say that good theories for practitioners would not also be useful for researchers; quite the opposite. As we describe, developing theories of teaching for teachers opens new lines of investigations for researchers.

Throughout this chapter, we use the terms model and theory as proposed by Praetorius and Charalambous (this volume). Following the Oxford Dictionary, they defined models as simplified descriptions of systems for assisting researchers in making predictions and theories as elaborations of models that describe the systems themselves—interrelated sets of ideas—intended to explain something of interest. Or, to quote another idea that strikes us as useful: “good theory helps identify what factors should be studied and how and why they are related” (Hill & Smith, 2005, p. 2).

Our analysis is shaped by our interest in understanding how classroom teaching can support students’ learning of valued content. We appreciate that the purposes of teaching include more than acquiring knowledge (Biesta, this volume) and that the theories of teaching can address more than its effectiveness (Herbst & Chazan, this volume). However, we believe there is value in theorizing about teaching effectiveness for learning content, especially in ways that are usable by teachers.

2 Moving Beyond a Simple Model of Teaching

Research on teaching has a long and illustrious history. It is fair to say that much of the work has treated as axiomatic the importance of investigating the effects of teaching on student learning outcomes (Floden, 2001). In fact, the credibility of theories of teaching is often based on whether the theory predicts learning outcomes (Farnham-Diggory, 1994; Herbst & Chazan, 2017). The basic model on which these theories are based looks roughly like the one pictured in Fig. 2.1. Teachers engage in teaching behaviors, and these behaviors impact what students learn. We know from value-added research that who students have as a teacher explains a good deal of the variance in how much they learn (Nye et al., 2004; Sanders & Rivers, 1996). It is reasonable to conclude that different teachers act differently, and that these differences help to explain what students learn.

Fig. 2.1

A simple, common model for research on teaching

The problem with this model is that it hasn’t worked very well. Despite decades of research, and many innovations in how researchers describe the “what teachers do” part of the equation, they have generally found very low correlations between teacher actions, on one hand, and what students learn, on the other (Brophy & Good, 1986; Dunkin & Biddle, 1974; Hiebert & Grouws, 2007; Oser & Baeriswyl, 2001). One of the largest and most ambitious studies conducted based on this model—the Bill & Melinda Gates Foundation Measures of Effective Teaching study—found few correlations between anything observable in teachers’ actions and the learning outcomes of their students (Kane et al., 2013; Kane & Staiger, 2010). This leaves Lucy Scott and her colleagues without much guidance for planning instruction that could predictably help students learn, say, to understand equivalent fractions.

Beginning in the 1970s, researchers recognized that the simple model’s lack of explanatory power could be attributed, at least in part, to the students’ role in determining what they learned from instruction (Doyle, 1977; Rothkopf, 1976). Students do not simply stand between teaching and learning as passive recipients but actively process information and represent events that unfold during classroom lessons. Even simple cognitive tasks require students to actively process information and formulate a response (Shulman, 1986). The mediating role that students play could be pictured by inserting a box between what teachers do and what students learn, as shown in Fig. 2.2. This elaborated model was proposed as a way to move beyond the simpler process-product model (Gage, 1972; Rosenshine, 1976) to represent the more complex relationship between what teachers do and what students learn.

Fig. 2.2

An elaborated model for research on teaching

Researchers often inserted into the middle box one or more variables intended to capture how students process instruction. By 1986, Wittrock (1986a) could review numerous efforts to identify variables that mediated the relationship between teaching and learning. Variables he labeled “thinking processes” included attention, comprehension, motivation, interpretation of feedback, self-concept, cognitive strategies, and metacognitive strategies. Some researchers gathered multiple cognitive variables and organized them into a “cognitive mediational paradigm” (Winne, 1987). Other researchers introduced constructs, like “student work,” to organize and interrelate the mediating effects of individual variables (Doyle, 1983, 1988). As Doyle argued, the work students do during instruction determines, to a large degree, what they will learn. Teaching that leads to one kind of work will yield a different outcome than teaching that prompts a different kind of work.

The idea of including mediating variables between what teachers do and what students learn has continued to influence the field today (Kyriakides et al., this volume; Scheerens, this volume). More complex models include different types of mediating cognitive variables (self-regulation, motivation, and engagement) as well as mediating social variables (teacher-student relationships, peer relationships, and family involvement (Cappella et al., 2016). These models, and the theories based on them, have generated numerous research programs providing important insights into teaching and learning (see Cappella et al., 2016).

Although we strongly endorse the insights that led to the creation of this mediation model (Fig. 2.2), we see two problems that have limited its success. First, the number of variables that lie between teaching and learning is almost limitless. The more researchers learn, the larger the number becomes. Isolating the effects of individual variables is of limited use because a single variable accounts for too little variance. But, studying the effects of collections of variables quickly introduces overwhelming complexity. Cooley and Leinhardt (1975) anticipated this problem by noting that “the vast array of possible influencing variables” in studies of teaching results in “an unmanageable quantity of data that has produced no clear insight as to what practices make a difference in student learning” (p. 4). The problem is exacerbated by the fact that individual variables do not independently exert their influence on instructional effects. Researchers must consider their interactions.

When examining the progress of research programs on aptitude-treatment interactions (ATIs), Cronbach (1975) noted that, even with a small number of variables, the number of interactions would take researchers into “a hall of mirrors that extends to infinity” (p. 119). Theorizing about, and researching, the mediational effects of large collections of individual variables is simply untenable.

The second problem with the mediation model is that there are few constraints on the nature of the mediating variables, and different researchers describe mediating variables of different grain sizes and different types. This makes it difficult for theorists to piece together findings across empirical studies to build coherent theories. Cronbach (1975), for example, reviewed the moderating effects that macro-variables, such as student aptitudes, have on the relationship of instruction to learning, whereas Winne (1987) argued for the importance of micro-variables, such as “rehearse the defining attributes of the concept” (p. 343). A wide range of mediating variables along the continuum are found in Wittrock’s (1986a) review, from motivation to students’ perceptions of teacher expectations to reliable counting strategies for solving beginning arithmetic problems. And, the elaborated mediation model proposed by Cappella et al. (2016) identifies macro-variables and micro-variables, both cognitive and social. To reiterate, we believe the concept of mediating processes has merit but the way in which it has been operationalized does not lead toward the development of theories that teachers could use to make daily instructional decisions.

3 An Alternative Model of Teaching

The importance of recognizing the impact of mediating variables cannot be overstated. The model in Fig. 2.2 has resulted in a number of fruitful programs of research. Yet, the more that is learned, the more we believe there is something missing that could simplify the sets of mediating variables without losing the insights they have provided. The missing construct, in our view, stems from the realization that what takes place in classrooms, as teaching unfolds, is not just the interplay of many variables but instead is the emergence of a stable system that defines the context in which learning takes place. This system, which we call sustained learning opportunities (or SLOs), is not just a bunch of variables but is a new construct that we insert between teaching and learning (See Fig. 2.3).

Before we present a more detailed description of the model, it is worth making a few general points. First, the term “sustained learning opportunities” should not be confused with common uses of “learning opportunities,” including its meaning of “curricular exposure” in international comparisons (McDonnell, 1995, p. 306). In addition, our use of “SLO” is very different than the acronym’s association with “student learning objectives” (https://texasslo.org/Resources).

Second, although SLOs are created by classroom variables and their interactions, they cannot be described in terms of these variables. Instead, a SLO is a system that needs to be described and understood in its own right. Because SLOs represent the sustained episodes in classroom lessons designed to help students achieve challenging learning goals, teachers recognize them more easily than individual mediating variables.

Third, teachers don’t single-handedly create SLOs. Instead, they orchestrate them, drawing on and coordinating all the resources they have to work with. These resources include curricula, but also include familiar cultural routines of teaching and learning and the beliefs that support these routines. Importantly, teachers do not create SLOs alone; students also play a role by participating in tasks and activities presented by the teacher (Schoenfeld, this volume; Vieluf & Klieme, this volume).

Fourth, we cannot overstate the importance of the word sustained. The learning opportunities that define students’ experiences and thus shape their learning are not just occasional events that happen by chance. If learning opportunities are not deliberately created and sustained over time, they are unlikely to affect students’ learning trajectories. Our interest is in understanding how students learn things that are hard to learn, that get mastered over long periods of time.

Finally, we want to highlight one of the most important features of the alternative model we are proposing. We have pointed out that SLOs themselves are a system, a construct worthy of a box. But we also see three more systems in Fig. 2.3 of which SLOs are only a part. All five components (three boxes and two arrows) comprise a system of teaching and learning. But the first three components (the first two boxes and the connecting arrow) comprise a system in its own right, as do the last three components (the second and third box and the arrow that connects them).

Fig. 2.3

An alternative model of teaching

Along with the construct of SLOs, it is this nested set of systems shown in Fig. 2.4 that capture the model’s most unique and significant contribution. In particular, our claim that the first and second box connected by the first arrow constitute a system of its own means that these components form a complete whole that can be analyzed and understood separately from the other systems. This, in turn, means that the quality of SLOs can be treated both as a dependent measure of one system—an outcome created by the curriculum and the teaching that brings the curriculum in touch with students—and as an independent measure of another system when used to predict learning.

Fig. 2.4

Two systems constitute the overall model

The nested characteristic of the model helps to conceptualize the relationship between theories and research on teaching with theories and research on learning. In our model, one theory is not embedded in the other (Openshaw & Clarke, 1970; Snow, 1973); rather, the theories intersect around the middle box. In order to trace relationships between what teachers do and what students learn, our model suggests that theories of teaching must be aligned with theories of learning at this point of intersection. This intersection is precisely what enables theories of creating SLOs to be useful for teachers. From their point of view, the SLOs that provide the goal for instruction are those that theories and research on learning have linked to the learning outcomes teachers want their students to achieve.

We believe the alternative model clarifies for theorists and researchers the task of building practical theories that can guide teachers’ day-to-day instructional decisions. Earlier, we pointed to the overwhelming number of individual variables in the mediation model that must be coordinated as a reason for searching for an alternative. With the diagram in Fig. 2.4, we can now see this problem from a new perspective. The traditional goal of connecting what teachers do with what students learn means documenting the connections across two distinct systems. On the other hand, building a theory of creating SLOs requires testing hypothesized connections within only the first system. Although it is true that traditional theories of teaching usually focus on the first arrow in Fig. 2.3, they often are required to explain the second arrow as well. We believe this poses a challenge that is too big for any theory that aims to support teachers’ decision making (Vieluf & Klieme, this volume; cf. Kyriakides et al., this volume).

3.1 Unpacking the Model

We turn now to unpack the model presented in Figs. 2.3 and 2.4. The model consists of three boxes connected by two arrows. It is worth pointing out that the arrows in our diagram do more work than the arrows in most diagrams. Instead of representing only a flow from one box to the next, the arrows represent the processes that create the complex relationships between the three boxes. The arrows represent verbs, the boxes represent nouns. The boxes are things that change only when teaching or learning change them. The arrows represent the processes of teaching and learning that produce the changes.

The First Box

The first box in our model consists of all the things teachers use to implement their lessons. These include written and supplementary materials (e.g., textbooks, pacing guides, concrete materials, lesson plans, etc.) designed by curriculum developers to create learning opportunities for students (Remillard et al., 2009), materials teachers create themselves, and materials they share locally and on the Internet. This is the raw material from which teachers draw as they select, adapt, coordinate, and implement sustained opportunities for student learning. In the previous models (Figs. 2.1 and 2.2) these things are left unspecified, though they clearly have a major impact on the kinds of SLOs teachers are able to create.

Also included in the first box are all of the teaching routines that are familiar to teachers, as well as all of the content, pedagogical, and cultural knowledge of teaching that teachers acquire while sitting in classrooms as students, engaged in teacher preparation, and working as teachers. Examples include the pedagogical content knowledge that assists teachers as they customize instructional activities for their students, and cultural knowledge that teachers use to create and sustain the daily classroom routines common within each culture.

The Second Box

The second box in our model represents the learning opportunities that students actually participate in and experience over sustained and repeatable segments of time. Sustained learning opportunities are the relatively stable times within classroom lessons during which students engage with an instructional activity designed to help them achieve a learning goal. The fact that they are relatively stable, even if only for a few minutes, means they can be identified and studied. They are visible within the fast-moving and fleeting interplay of variables within classrooms.

A SLO emerges from the interaction of classroom variables as a signature characteristic of the lesson that matters most for students’ learning. It derives its impact (and predictive power) from the way in which the variables interact to create its effect, not from its size or intensity. More is not necessarily better. The final quality of the SLO is determined by the interactions among the primary players—teacher, students, and content (Cohen et al., 2003; Lampert, 2001).

Indeed, a SLO could be thought of as a dramatic play. Putting on a play requires the coordination of many elements—sets, scripts, and actors, to name a few. The quality of the play cannot be judged by each of its elements evaluated individually but rather by the emergent qualities of the event that results from the interplay of these elements. Teachers and students are actors in a kind of play. They each must work to enact the play, to create a briefly-sustained temporary world in the classroom. In the case of a SLO, each actor learns from their experiences as they participate in the world they have created together.

We can clarify further the SLO construct by comparing it to related constructs. As noted earlier, we can distinguish SLOs from “opportunity to learn” (OTL). OTL represents content covered and/or the tasks presented to students (see McDonnell, 1995, for a history of OTL and Travers, 1993, for its use in SIMS). And, opportunities presented are different than opportunities experienced (Biesta, this volume; Praetorius et al., 2020; Vieluf & Klieme, this volume). A related distinction can be made between SLOs and the “enacted curriculum” (Remillard & Heck, 2014; Stein et al., 2007; Thompson & Usiskin, 2014). The emphasis in discussions of the enacted curriculum is often on the teaching moves and behaviors that transform the written curriculum into the learning opportunities that reach the students. SLOs emphasize the opportunities that emerge and are experienced by students as they participate in the enactment.

The construct we see as closest to SLOs is the construct of classroom tasks described by Tekkumru-Kisa et al. (2020). In their formulation, a classroom task “creates the context within which students think about the subject matter” (p. 607). Tasks move through four phases during a lesson (the life of a task). We connect the SLO construct to the third of their four phases: “the task as perceived by each student and as enacted by the teacher and the students is the actual intellectual work in which students engage (i.e., the level and kind of student thinking happening during the lesson)” (p. 607).

The Third Box

The third box consists of student outcomes, the most prominent of which is student learning. In this chapter, we focus on learning outcomes aligned with academic or content goals. Changing the focus to other goals that societies, and teachers, often value might change what would fit into the components of our model but would not change the model itself (see Biesta, 2016, this volume, and Lampert, 2001, for examples of other important goals, such as students’ forming identities as autonomous learners). It is also important to note that we include both immediate and long-term goals in this box.

The First Arrow

The first arrow in our model includes much of what researchers and educators ordinarily think of as teaching. However, it includes more than the visible, public actions of teachers as they implement a lesson. It also includes planning for a lesson and reflecting on a lesson after it is taught. It represents all of the processes teachers use to turn the intended curriculum into the enacted curriculum—the curriculum that is presented to students. “The teacher is an active designer of curriculum rather than merely a transmitter or implementer” (Remillard, 2005, p. 214).

We focus on planning, implementing, and reflecting because we see them as the minimum processes needed to represent what the teacher does to create SLOs. We recognize that what is involved in these activities can be unpacked in different ways and at various levels of detail (Cai et al., this volume; Scheerens, this volume; Schoenfeld, this volume). In fact, any single chapter cannot do justice to all the ingredients that fit into this arrow (Ball & Forzani, 2009; Grossman, 2020; Lampert, 2001). Also, although the arrows in our model flow from left to right, we can imagine processes that flow in the opposite direction as well. What teachers and researchers learn from implementing curriculum and observing the sustained learning opportunities, for example, could have a “backward design” effect on the way in which the curriculum is revised and improved (Wiggins & McTighe, 2005).

The Second Arrow

The second arrow represents the processes and cognitive mechanisms that transform learning opportunities as experienced by students into learning outcomes. Like the first arrow, it links two boxes to form a separable sub-system, this time consisting of interrelated elements that turn sustained learning opportunities into learning outcomes as assessed by a wide range of measures. The arrow establishes the types of SLOs that will become the targets teachers use to plan and implement instruction.

Establishing connections between particular types of SLOs and particular learning outcomes is usually the work of researchers. Researchers, however, are not the only ones who can contribute to educators’ understanding of the second arrow. Teachers learn about processes that produce student outcomes, for example, when they use formative assessment tools to get a sense of what their students are thinking and learning from the opportunities they experience (Silver & Mills, 2018; Wiliam, 2018), or when they review students’ work to get a more detailed look at students’ conceptions and misconceptions (Kazemi & Franke, 2004), or when they administer and grade quizzes and exams to find out what their students learned during the lesson(s). Unfortunately, the culture and practices of education research in the U.S. do not yet include a mechanism for routinely capturing this information.

Even though teachers do not usually contribute to more generalized knowledge connecting SLOs with learning outcomes, they frequently use what they learn from assessing outcomes to reflect on the effectiveness of their teaching. Although teachers’ reflections are part of the work of teaching, and so belong squarely inside the first arrow, they also could contribute to our understanding of the second arrow. This highlights the fact that the boundaries separating the two systems are not impermeable. There are places where work on teaching and work on learning can and should overlap (Romberg & Carpenter, 1986).

Connecting the Two Systems

The ability of researchers to document links between SLOs and learning outcomes is crucial for the model shown in Figs. 2.3 and 2.4 to function as we propose. With these links established, the work of teaching represented by the first arrow could set a goal of creating SLOs that have been shown to align with desired learning outcomes. Teachers could focus on creating SLOs with specific features if they could assume that opportunities with these features led to the learning outcomes they intended.

It turns out that researchers have reported compelling evidence that links types of SLOs and particular learning outcomes (Bjork & Bjork, 2011; Cai et al., 2020; Hiebert & Grouws, 2007; Richland et al., 2012). Consider the case of mathematics. If we specify understanding of key concepts as an important mathematical proficiency and a desired learning outcome, we can identify two features of a SLO that enable this outcome. A first feature is often referred to as productive struggle (Hiebert & Grouws, 2007). Mounting evidence from the learning sciences indicates that deep and lasting learning results more often from periods of struggle and confusion than from smooth error-free learning or from the kind of Eureka! moments educators strive to create (Harackiewicz et al., 2008; Kapur & Bielaczyc, 2012). Robert and Elizabeth Bjork coined the term “desirable difficulties” to refer to a body of research showing that introducing difficulties into the learning process can produce deeper and longer-lasting learning, despite the fact that students often describe the experience as less enjoyable and believe that they have learned less (Bjork, 1994; Bjork & Bjork, 2011). If mathematics educators want students to understand a concept, they must find ways to engage students in struggling to make sense of the concept.

Of course, struggling by itself won’t produce deep learning of significant mathematics. The struggle must be focused on the right things. This leads to a second feature of SLOs that predict conceptual learning outcomes: explicit connections (Hiebert & Grouws, 2007). To develop understanding, students must focus their efforts on making the connections that lend coherence to a domain and that result in knowledge that is both flexible and transferable. In particular, students must work to forge connections among core concepts, representations, and the world to which the concept applies (Fries et al., 2020; Hiebert & Carpenter, 1992; National Research Council, 1999, 2001; Roth & Garnier, 2006). These connections don’t usually spring forth spontaneously. They must be made explicit, by students or the teacher, and they must be made at the right time, when students are prepared to recognize and construct these connections for themselves (Dewey, 1910). Explanations, comparisons, analogies, and visual representations are all tools that teachers can incorporate into SLOs that help students create connections and develop deeper understanding (Richland et al., 2004, 2012).

As we noted earlier, learning things that are hard to learn requires SLOs to be sustained over observable periods of time. To develop conceptual understanding, students must practice struggling productively with making important connections in the domain. Because this is not the usual form of practice, often called repetitive practice, it has been labeled deliberate practice, a term that comes from research on expertise (Ericsson, 2006). Deliberate practice involves a planned sequence of opportunities that stretch over more than one lesson, sometimes over many lessons. In fact, researchers have reported the kinds of sequential variation in mathematical problems that create these SLOs (Carpenter et al., 2017; Clements & Sarama, 2014; Fries et al., 2020; Huang & Li, 2017; Kullberg et al., 2017; Pang & Marton, 2009). Treating SLOs as the proximal goal for teaching depends on documenting more connections between features of SLOs and desired learning outcomes.

3.2 An Advantage of the Model for Teachers (and Researchers)

A driving motivation for writing this chapter was to explore whether reimagined theories of teaching could be more useful for teachers. By dividing the larger system of teaching and learning into two smaller systems, we have imagined a way for theorists and researchers to narrow their focus to one system or the other. This, we argue, can suggest new lines of research that previously might have been hidden by the expectation that researchers trace transformations from the written curriculum through the enacted curriculum, through the learning opportunities experienced by students and, finally, into learning outcomes. Research questions change if one works within a system (Fig. 2.4). As just noted, for example, research in System 2 can focus on connections between SLOs with particular features and desired learning outcomes. Lines of research in System 1 could focus on describing the classroom conditions that yield SLOs with particular features.

Theories of creating SLOs offer teachers a clear theory of what they need to create and what their creations should look like as they implement instruction. While teachers are implementing instruction, it is almost impossible to keep their eyes both on the instruction they are enacting and the evidence needed to judge whether students are achieving the learning goals of the lesson. Although still challenging, it is conceivable that teachers could monitor students’ immediate responses to the learning opportunities being enacted because these are proximal to implementing the planned opportunities. Based on these responses and on theories of creating SLOs, teachers could adjust instruction to improve the quality of SLOs (see Biesta, this volume).

Walter Doyle previewed this idea more than four decades ago when assessing the usefulness of the process-product framework (similar to the simple model—in Fig. 2.1):

In the event that the presentation did not accomplish its objective, the process-product formulations would offer no further guidance. Just knowing the relation of a technique to terminal performance fails to supply sufficient information about immediate contingencies in the classroom (Doyle, 1977, p. 126).

He then said that if teachers could focus on activating an intermediate response from students, they could “experiment” with instructional strategies to see which worked best. This, Doyle (1977) said, “enables a teacher to practice what Cronbach (1975) has called ‘short-run empiricism,’ in which one monitors responses to the treatment and adjusts it” (p. 126).

To reiterate, a theory of SLOs and how to create them could open new lines of research and could help teachers know what to look for when observing students’ responses to instruction and what changes they might consider as they seek to improve the quality of the SLO they are creating. A theory of creating SLOs is our answer to the question posed in the first paragraph of this chapter: “Are there theories that could help Ms. Scott predict, for example, what might happen if she chooses one task vs. another?” We believe our alternative model of teaching could spawn theories of creating SLOs that are usable by Ms. Scott and her professional colleagues.

3.3 Limitations of the Model

Although we believe our model of teaching and learning captures meaningful aspects of teaching and provides teachers with a manageable system to which they can apply their efforts to improve, even this alternative model includes only a fraction of the full system of teaching. One only has to look through the extensive Handbooks of Research on Teaching (3rd edition, Wittrock, 1986b; 4th edition, Richardson, 2001; 5th edition, Gitomer & Bell, 2016) and the chapters in this volume to see the vast and rich legacy of relevant research and theory that address various aspects of the immensely complex system of teaching. Our model does not touch many factors, both outside and inside the classroom, that contribute to students’ experiences in school (Cobb et al., 2018; Cohen, 2011; Creemers & Kyriakides, 2008; Kyriakides et al., this volume; Lampert, 1985, 2001).

We acknowledge that our model is located within a much larger multi-level system of schools, districts, and so on (Cobb et al., 2018; Scheerens, this volume; Scheerens et al., 2003; Strom et al., 2018), all of which impact teaching in some way. We attend to only a small portion of these factors and to only one level of the system of schooling. Because of the mind-bending complexity of teaching, everyone who wades into this domain must find ways to simplify the problem and put boundaries on their search for solutions, leaving large portions of the domain untouched. We are no exception.

One of the challenges facing those who presume to investigate teaching is how to simplify teaching to make it more tractable without, at the same time, losing its essential character. Grossman and McDonald (2008) express the challenge this way:

A framework for teaching would require a careful parsing of the domain …. This effort to parse teaching would need to respect the difficulty of breaking apart such a complex system of activity and the dangers of doing irreparable harm to the integrity of the whole by making incisions at the wrong places (p. 186).

We sought to strike this balance between simplification and ecological validity in two ways. To simplify, we chose to focus on the major components of teaching that commonly fall under the control of educators whose work is purposefully directed toward improving teaching and learning. Classroom teachers, instructional leaders, curriculum developers, and education theorists and researchers, all fall into this group. To retain ecological validity, we preserved minimal elements of a system of teaching, as we understand it. Within this system, we focused on those factors that are of most concern to classroom teachers and over which they have some control. We wanted, in other words, to specify a model that could generate theories that would be useful for Lucy Scott and her fellow teachers.

4 Building and Using Theories of Creating Sustained Learning Opportunities

We turn now to discuss theories that could be built using the model shown in Figs. 2.3 and 2.4. We focus here on the first system in the model, the system that turns written curriculum and other teaching resources into specific types of SLOs linked with particular learning outcomes. We reflect on what this process might look like—what the main elements of such theories would be, and how the elements might be related. Our aim is to develop what Hill and Smith (2005, p. 2) called a “good theory”: one that “helps identify what factors should be studied and how and why they are related.” We start by presenting a sample hypothesis that illustrates the nature of these theories. We then imagine the kind of work researchers and teachers might do to build and use theories of creating SLOs.

4.1 A Sample Hypothesis in a Theory of Creating Sustained Learning Opportunities

Theories are built from a set of related hypotheses. One hypothesis that could be part of a theory of creating sustained learning opportunities is what we call the struggle-first hypothesis. Based on analyses of Japanese mathematics classrooms and on experimental research carried out in the United States, this hypothesis suggests that students will create connections among concepts more effectively if they engage in productive struggle before they are given direct instruction than they would if the direct instruction came first. When students are given direct instruction first, says the hypothesis, it removes the motivation to struggle because students already have the solution they need, thus short-circuiting the deeper learning that can occur during productive struggle.

It is worth noting how the struggle-first hypothesis differs from the mediating variables approach alluded to earlier. It we took the mediating variables approach, we might identify productive struggle as an important variable to measure. But simply measuring the amount of struggle in a lesson would not take into account the importance of how the struggle fits within a SLO. The same mediating variables can take on different meanings when they are part of different lessons (Janssen et al., 2015), a fact that becomes even more salient when comparing lessons across countries with different pedagogical traditions (Stigler et al., 1996; Stigler & Hiebert, 1999). Many variables, in addition to productive struggle, have been found to have different effects when embedded in different pedagogical systems (e.g. Kawanaka & Stigler, 1999).

The struggle-first hypothesis was initially formulated by researchers, and researchers have generated empirical evidence in support of the hypothesis. But to be useful for teachers, the hypothesis needs to be elaborated. Numerous secondary hypotheses need to be generated, tested and refined before the struggle-first hypothesis could guide teachers’ actions across a wide variety of contexts and content. Because this variation in context occurs in classrooms, teachers must be part of the work that formulates, tests, and refines the hypotheses. As researchers and teachers flesh out the struggle-first hypotheses, they might ask questions such as, “What kinds of tasks work best for students who are encountering the topic for the first time?” or “What kinds of tasks work best for specific connections between core concepts of a specific content domain?”

It might be that beginning students struggle most productively to make connections when they are solving problems that have a particular level of cognitive demand (Stein & Lane, 1996; Tekkumru-Kisa et al., 2020), or with tasks that vary in particular ways from tasks students already have completed (Huang & Li, 2017; Marton, 2015; Pang & Marton, 2009). Teams of researchers and teachers might focus their classroom investigations on how the task is initially presented to students, often called the “launch” (Wieman, 2019); or on how subsequent class discussions should be orchestrated during and after the task is completed (Smith & Stein, 2018); or on the role of well-timed hints (Stigler & Hiebert, 1999); or on how best to sustain students’ efforts to complete the task in the face of difficulties, and perhaps frustration (Mukhoiyaroh et al., 2017; Tulis & Fulmer, 2013).

These are just a few of the hypotheses that teams of teachers and researchers could generate and investigate. These secondary hypotheses get filled in and refined as teachers experiment with different strategies in their classrooms to shape the learning opportunity so students derive maximum benefit from productive struggle. Formulating, testing, and refining hypotheses is an iterative process that engages teachers and researchers in the kind of cause-effect reasoning that is essential for improving teaching. Notice also that these secondary hypotheses represent only a fraction of the work needed to elaborate and refine the main hypothesis; they focus only on the “struggle” part of the struggle-first hypothesis. Teacher-researcher teams must formulate and test additional hypotheses to explore the best ways to help students make explicit the connections that complete this sequence.

As teachers test secondary hypotheses in their own classrooms, researchers can gather the findings and look across classrooms for patterns in what teachers do and how students respond. Are there ways of implementing a task, for example, which leads to productive struggle for most students in most classrooms with specific characteristics? As researchers guide the refinement of secondary hypotheses by organizing the incoming results, sharing them with other researchers working on similar problems, and suggesting other forms of these secondary hypotheses for teachers to test, a mini-theory begins to take shape around how to create SLOs that support making key connections through productive struggle.

Other primary hypotheses, such as “understanding requires repeated struggle,” trigger the development of other mini-theories that guide, for example, the sequencing of tasks and activities both within and across lessons. As mini-theories begin forming around hypotheses that fit together, the mini-theories expand in scope and incrementally move toward larger theories of creating SLOs. Although building these mini-theories takes considerable time (years rather than weeks or months), the work of teachers and researchers can be accumulated, coordinated, and aggregated to gradually but steadily move toward more useful theories of creating SLOs.

As a mini-theory is forming for how to create productive struggle with making key connections, one can imagine teachers drawing on the mini-theory as they plan a lesson. As teachers internalize the mini-theories, they will be able to represent them as mental models. Teachers can run these mental models during planning as a means of predicting what the consequences will be as they weigh various options for an upcoming lesson. As the mental models become richer and stronger, teachers will be able to run their mental models on the fly, as they teach, as a means of predicting how students with different characteristics will respond to different parts of a lesson. As teachers practice making and testing predictions of this sort, they are engaged in a high-quality professional learning process that some authors have referred to as deliberate performance (Fadde & Klein, 2010).

4.2 Imagining the Work of Building Theories of Creating Sustained Learning Opportunities

The problem of how best to build theories of teaching has received relatively little attention (Praetorius & Charalambous, this volume). There are no clear precedents to follow as we outline a possible path for building theories of creating SLOs. Nevertheless, we move beyond the example just presented and propose some general processes and guidelines that could help build these theories in order to provide a more complete picture of the theories we have in mind.

We begin by asking, “If theorists and researchers wish to create and test theories of SLOs, what might they encounter and how might their work lives change?” Although this kind of work has not been attempted in any kind of serious way, it might be useful to imagine what kind of work would be entailed in order to envision the kinds of changes researchers could expect. We can identify several changes that researchers, and teachers, might decide to make. But, we anticipate there are many more and each of the ones we identify would likely have ripple effects through the educational system.

Changing Roles for Teachers and Researchers

Researchers and teachers have long worked toward different goals and have played different roles in the educational system. Our example of building even a mini-theory around the struggle-first hypothesis suggests that these groups might need to adopt shared goals and change their professional roles (and identities).

For some time, the field has recognized that it is ineffective for researchers to develop theories and then hand them to teachers. Researchers simply don’t know enough about the processes and conditions that determine how teaching behaviors and routines work to create SLOs in classrooms. In a field such as education, where good practices can run ahead of good theories, “the experience and intuition of practitioners” becomes especially important (Lipsey, 1993, p. 12). If researchers want to be better positioned to engage seriously in solving problems of practice (Burkhardt & Schoenfeld, 2003; Cai et al., 2018; Cohen & Mehta, 2017) they will need to find ways to blur the boundaries between themselves and teachers (Akkerman & Bakker, 2011; Cai et al., 2018, this volume; Cohen-Vogel et al., 2015; Penuel et al., 2011). Perhaps researchers will find ways to work side-by-side with teachers to ensure they are addressing instructional problems that teachers actually face as they implement and evaluate learning opportunities.

We can envision three unique roles for researchers to play. First, they could suggest hypotheses for how SLOs with particular features might be created. “Struggle-first” was formulated by looking across multiple settings, even multiple cultures. Teachers are not usually in a position to do this work, but researchers are. They could look across classrooms and search for patterns in the effectiveness of various teaching behaviors for creating similar SLOs and, conversely, they could search for patterns across classrooms in the conditions that turn similar teaching behaviors and routines into different SLOs. Second, researchers could identify prior research that would provide a starting point for teachers’ work on developing the types of mini-theories outlined above (see the citations in the earlier example of “struggle-first”). Third, researchers could interpret data on learning outcomes that emerge across classrooms in order to evaluate and refine the links between features of SLOs and learning outcomes (the second arrow in Figs. 2.3 and 2.4).

Teachers might want to expand their traditional roles as well. Teachers uniquely have intimate knowledge of their students, enabling them to both formulate predictions and test the predictions by observing students’ responses to instruction. This is not new work for teachers. They constantly make predictions, often intuitively and tacitly, about how students are likely to respond to particular instructional activities. However, making these predictions purposefully and explicitly would be new for most teachers. Similarly, the observations needed to test predictions about SLOs are different than the kinds of observations teachers make every day. We could imagine that teachers who are involved in this work would gradually adopt an experimental orientation toward their work (Hiebert et al., 2003). By experimental orientation, we mean simply learning from “experience carefully planned in advance” (Fisher, 1953, p. 8) and bringing the power of causal thinking into their practice (Gallimore et al., 2009).

Imagine teachers and researchers developing teams, or partnerships, to meet the challenge of creating theories of SLOs. The promise of researcher-practitioner partnerships has been realized in professional fields outside of education (Bryk et al., 2015; Morris & Hiebert, 2009, 2011). From auto manufacturing to the repair of Xerox machines to clinical medicine to the wind turbine industry, this multiple expertise model has been used effectively to improve practices across a range of professions (Douthwaite, 2002; Gawande, 2007; Kenney, 2008; Langley et al., 2009; Rother, 2009). When teachers and researchers form partnerships around shared problems of practice, they can realize similar successes (Bicknell & Young-Loveridge, 2017; Coburn & Penuel, 2016; Donovan & Snow, 2018; Quartz et al., 2017).

The challenge for teacher-researcher partnerships would be to retain the richness and ecological validity of the information from individual teachers’ classrooms while surmounting the contextual uniqueness of each classroom. Every teacher faces somewhat different challenges because there are many factors that influence how students take up the opportunities teachers intend (Biesta, this volume; Clarke et al., 2006; Nuthall, 2004; Stigler & Hiebert, 1999; Vieluf & Klieme, this volume). The same teaching moves that work in one classroom might not work in another classroom. And, somewhat different teaching moves might be needed in different classrooms for students to experience the same learning opportunities.

Researchers will need to find ways to aggregate what is learned by multiple teachers across many classrooms into more generalized hypotheses that can provide guidance to all the teachers trying to solve the same instructional problem. The concept of “networked improvement communities” (Bryk et al., 2015) will undoubtedly play an important role in gradually formulating generalized hypotheses that can guide teachers’ predictions. Researchers will play an especially important role in looking across classrooms for patterns that link particular teaching moves with desired learning opportunities. However, it is too early to speculate how these approaches will play out and what additional, perhaps still unknown, approaches might be needed.

It goes without saying that changing roles in these or other ways is not trivial for either group (Cai et al., 2018; Yurkovsky et al., 2020). But, teachers and researchers might decide it is worth the effort if they see the payoff in sustainable improvements in teaching and richer learning for students.

Slowing Down the Cycle of Teaching

In addition to changing the roles of teachers and researchers, building theories of creating SLOs will require slowing down, at least for some lessons, the common cycle of planning, implementing, and reflecting on classroom lessons. These activities are part of the work teachers do every day, but planning and reflecting are often done quickly, sometimes only as teachers enter and leave classrooms. This is not sufficient because building, using, and refining theories takes time—at the moment and over the long run. Teachers who invest in this work will need time to plan and reflect on specially targeted lessons each year.

Of course, teachers would not be able to make this happen on their own. Educators at various levels of the larger system (e.g., building and district administrators) would need to create the time and space for teachers to do this kind of work. Additional time would be needed even though it would not be necessary to slow down the cycle of teaching for more than a few lessons each year. The goal is not the creation of a full curriculum of lessons, but the development of theories that can be applied across multiple lessons. Over time teachers’ work could be accumulated to yield gradually improving theories of creating SLOs.

Planning and Predicting

Thoughtful planning of a lesson necessarily involves anticipating how students will respond to particular instructional tasks. A natural way for teachers to anticipate students’ responses is to run the lesson in their heads, imagine how students will respond at key moments, and adjust their plans accordingly. Because teachers’ knowledge is often implicit, they will need to work with researchers to make explicit the hypotheses that underlie their predictions.

A teacher might hypothesize, for example, that students’ will engage more with an initially-challenging problem if they see how it relates to a similar problem they have recently learned to solve. A researcher could help to clarify the hypothesis and design an experiment that could lead to useful information related to the hypothesis. The teacher could then select or design specific tasks that would work within the research design. In this way, designing, implementing, and observing students’ responses to a task is not only an act of teaching by teachers, but one of hypothesis testing by teachers and researchers.

Although anticipating how students will respond at key moments in a lesson is often something teachers do subconsciously, it is not always easy. Teachers, especially those with experience and especially as they get to know their students well, are likely to have good intuitions about how their students might respond to particular tasks. But, forming predictions about students’ thinking during lessons across a range of topics will be difficult. Fortunately, teachers (with researchers’ help) can draw ideas from the long and rich legacy of research on teaching and learning to formulate predictions about students’ thinking in particular task situations.

In highly researched domains, such as mathematics, the predictions that teacher-researcher partnerships make can be informed by research findings that detail students’ likely ways of thinking about problems of various types. For example, research on young children’s arithmetic performance provides primary grade teachers with information on likely solution strategies children might propose to most arithmetic problems if teachers present them in certain sequences (Carpenter et al., 1996; 2014; Sarama & Clements, 2009). Teachers can use this information to do more than predict students’ thinking; they can use it to select mathematical problems and implementation strategies that are likely to engage students in the intended SLOs (Carpenter et al., 2014; Clements et al., 2020). Promising work on learning trajectories provides increasingly fine-grained descriptions of children’s thinking and could be used by teachers to plan instruction on some topics (Clements & Sarama, 2014; Clements et al., 2004; McGatha et al., 2002; Steffe, 2004).

Before moving to the second phase of the cycle, we should clarify the nature of the hypothesis testing process we are describing. We do not want to enter the continuing debate in education about the most useful methods for improving practice (Bulterman-Bos, 2008; Jacob & White, 2002; Moss et al., 2009) but rather want to alert the reader that we have in mind the kind of “short-run empiricism” (Cronbach, 1975) or “piecemeal tinkering” (Popper (1944/1985) that involves repeated small tests of small changes (Morris, 2012; Morris & Hiebert, 2011). In this approach, a hypothesis is formulated about the relationship between teachers’ actions in the classroom and the SLO that is created, predictions are made about how students will respond, and just enough data are collected to assess the viability of the hypothesis. Proposed by Popper (1944/1985) as the best scientific method for improving socially-embedded professional practices, we see this kind ofsmall-scale hypothesis testing, with accumulation of results over multiple replications, as an appropriate method for teacher-researcher partnerships to employ.

Implementing and Observing

The point of making predictions about the SLOs students will experience is to set up the next phase of the cycle—observing the impact of the implementation and assessing the accuracy of the prediction. Whether predictions are accurate is, of course, an empirical question. Predictions must be tested and then hypotheses refined. To build theories of creating SLOs, checking the predictions means observing the kinds of learning opportunities experienced by students.

Not just any observations will do. Needed are observations focused on whether the learning opportunities that were experienced by students possessed the desirable features identified during the planning phase, and whether changes in instructional choices (e.g., of the task presented) improved the quality of students’ experience in the predicted ways. Because students’ experience is mainly an internal affair, it is not easy to draw completely accurate conclusions. Observing the individual responses of 30 students and trying to accurately infer what they are thinking is unrealistic. Teachers’ judgments will be estimates, without the psychometric properties of systematic and formal assessments. Over time, however, repeated judgments by skilled teachers will lead toward accurate-enough inferences. It is useful to remember that researchers have long called for teachers to make instructional decisions based on inferences about students’ thinking (Carpenter et al., 2014; Dewey, 1929; Lampert et al., 2010; Nuthall, 2004; Wittrock, 1986a). We are simply suggesting that these inferences be made based on planning and thoughtfully considered purposes.

Imagine Lucy Scott presenting a cognitively demanding task on equivalent fractions and observing whether her students are engaged in productive struggle to connect the concept of equivalence with the numerical patterns in the written fractions. What might she look for? It is first important to recognize that, if it is possible to make accurate-enough observations, Lucy Scott is the person who could make them. Observing and interpreting students’ behavior with reasonable accuracy requires extensive knowledge of students’ past performance, their tendencies to respond to new challenges in particular ways, what their outward behaviors indicate about their internal struggles, and so on. Ms. Scott is the only person with this kind of intimate knowledge of her students.

Because productive struggle involves particular kinds of work, there are guidelines that Ms. Scott could use when observing her students. She could look for whether her students were wrestling with the task—(not immediately finding the answer but continuing to try), whether they were asking questions that were relevant to the key ideas of equivalent fractions, whether they were experiencing moments of confusion but sustaining their efforts, whether they were developing partial solutions that were on the right track (Brown, 1993; Ermeling et al., 2015; Hiebert et al., 1996; SanGiovanni et al., 2020).

In addition, teachers like Ms. Scott are likely to find that their observations of students’ responses are enabled by the planning they did during the first phase of the cycle. Along with planning instruction, teachers can plan what kinds of observations they need to test their predictions. In some cases, what teachers look for will be visible (for example, in students’ written work, or in their behavior while solving a problem); in other cases, teachers will need to elicit student thinking (for example, by asking pointed questions and asking students to share their thinking). The more that teacher-researcher partnerships learn, specifically, about the manifestations of productive struggle with equivalent fractions and with other topics, the more informed will be the guidelines for observing student responses.

Reflecting and Refining

The third phase in the cycle of teaching is reflecting on the observations made during instruction in light of the predictions that were posed. Teachers frequently reflect on the success of a lesson but often do so quickly and without much thought. Participating in a teacher-researcher partnership and using a theory to guide reflection encourages teachers to slow down the process and make it explicit and systematic. As with planning and observing, theories play an important role in the reflecting phase of the teaching cycle. In the reflecting phase, teachers and researchers can work together to figure out how the results of a lesson can be used to revise a particular hypothesis or to suggest the creation of new hypotheses.

Looking back to see links between teaching strategies used during the lesson and learning opportunities experienced by students would enable researchers and teachers to examine the accuracy of their predictions, to learn from “experience carefully planned in advance” (Fisher, 1953, p. 8). It would reinforce for everyone the realization that the lessons for which they choose to slow down the teaching cycle are carefully planned experiments that can be seen through a cause-effect lens (Gallimore et al., 2009).

Because predictions are based on unproven hypotheses, many of the initial versions will not be very accurate. However, over the years, as researchers and teachers become more explicit about their predictions, gather more information, and reflect on this information to propose revisions, the soundness of the hypotheses and the accuracy of the predictions will gradually improve. As researchers gather information provided by individual teachers, examine emerging patterns, share these with other partnerships and suggest additional tests of best predictions, the robustness of hypotheses will grow and theories could be gradually built and refined.

To reap the benefits of many teachers individually testing and refining hypotheses, and many researchers assisting with gathering, organizing, and analyzing incoming data, there must be ways to record, store, and share the ongoing findings and the best current practices. This brings us to our third big change that teachers and researchers might make if they become invested in building theories of creating SLOs.

Creating Artifacts

Long ago, Dewey (1929) observed that one of the saddest things about American education is that teachers take their best ideas with them when they retire. Educators have no good way to preserve what individual teachers learn from their experience. Thousands of teachers like Lucy Scott drive to school every day ready to tackle similar instructional problems (e.g., how to help students understand equivalent fractions), but the current education system in the U.S. provides no way to record and share their hypotheses, predictions, and observations so as to benefit other teachers and their students (Rothkopf, 2009).

A promising approach to recording, preserving, and sharing information across classrooms is to agree on an artifact into which teacher-researcher partnerships could record what they learn from the process we have described. A variety of artifacts are possible, including a record of the presentation of a particular task plus the ways in which students work on the task. Tekkumru-Kisa et al. (2020) argue that examining “the enactment of a particular task, from beginning to end … allows researchers to see, organize, and analyze students’ opportunities to learn in meaningful ways” (p. 607). For us, however, lesson plans have a special appeal (Morris & Hiebert, 2011, 2015; Stigler & Hiebert, 1999). Cai et al. (this volume) recommend a similar artefact using a different name, “teaching cases”). For one thing, lesson plans are written at a grain size that is recognized across countries and cultures. Based on our analyses of the TIMSS Video Study lessons, we believe it is the smallest unit of instruction that preserves the system of creating SLOs (the system of teaching in Fig. 2.4) (Stigler & Hiebert, 1999). Although a single lesson usually does not develop a mathematical topic fully, it can be analyzed as a unit that stands on its own.

Teachers might find that written lesson plans have several advantages as a shared artifact (Morris & Hiebert, 2011). Because almost all teachers use lesson plans in some form, they are a familiar instructional tool indexed to content topics. By annotating lesson plans with the current and best teaching strategies for that lesson, teachers have access to this knowledge just when they need it. This knowledge consists of the most refined predictions at the time for how to create SLOs that have been found to help students achieve the lesson learning goals(s) along with the hypotheses that provide the rationale for these predictions. Accessible rationales increase the likelihood that the strategies will be implemented as intended and decrease the likelihood that future predictions will repeat the same mistakes as previous predictions.

Lesson plans also provide a natural receptacle for what partnerships learn as teachers enact the plans. And, because annotated lesson plans provide a storage place for knowledge, they can carry the profession’s memory, providing a way for new teachers to pick up where the previous generation left off. Shared, updated lesson plans can prevent the profession from suffering “collective amnesia” (Shulman, 1987, p. 11), forcing every new teacher to start over. John Dewey would be pleased.

Finally, lesson plans provide a type of an instructional artifact around which teachers, researchers, and others with relevant expertise can collaborate to solve common instructional problems (Morris & Hiebert, 2011). Modifiable, shareable artifacts uniquely enable collaborative learning by becoming the public focal point for the exchange of information and ideas (Bereiter, 2005). A consequence of this collaborative activity is that teachers could experience a cultural shift from treating teaching as an individual private enterprise to treating it as a collaborative, public, and reflective activity. This would be a significant change, in part because it can encourage teachers to recognize they are capable of sustained growth as true professionals (Franke et al., 1998).

5 Conclusions

We have proposed a new conceptual model to guide research on teaching and learning. Although we built on the groundbreaking work of others who explored the idea of mediating variables between teaching and learning, our conceptualization is not common. Many researchers and practitioners still imagine that researchers will discover links between what teachers do and what students learn, with perhaps some mediating variables in between. Given the historical challenges of applying this traditional model to the day-to-day problems of classroom practice, we proposed an alternative model as a way to move theories of teaching closer to the work of Lucy Scott and her colleagues. Rather than trying to extract more from the traditional models, we believe efforts would be better spent fleshing out the alternative model that sets SLOs as the proximal goal of teaching.

The brief descriptions we have provided of the model, of the theories that could be built from the model, and of the processes that might be used to build the theories are intended to provide a glimpse into the possibilities. But the descriptions do not resolve many issues of which we are aware and even more issues that are sure to arise. It is clear that, in addition to the massive work that will be required to build out theories of creating SLOs, more work will be needed within the second system in the model (Fig. 2.4)—the transformation of SLOs into learning outcomes. More complete and better specified theories of learning are needed to tie SLOs to learning outcomes. These theories will require more sophisticated ways of defining and assessing what SLOs could look like in classrooms. Because theories of creating SLOs are dependent on specifying their features and linking them to well-defined learning outcomes, work within both systems must proceed together.

If the model we have proposed is taken seriously, researchers and teachers will need to work together to explore its ramifications and to build useful theories of creating SLOs. We have described some possibilities of the form this work might take, but we are curious to see what conditions teachers and researchers decide are critical for doing this work and for sustaining it over the time.

It is too early to make claims about the ultimate impact of this work, but we believe it is sufficiently promising to warrant serious attention. We recognize this is not a quick fix for putting useful theories into the hands of teachers. It will take years to see the payoffs in terms of student learning gains. As one anonymous reviewer of this chapter phrased it, “the promise of this work will depend on how it gets taken up, developed and elaborated.” This can be, by itself, a reason to not take the model seriously.

Following the TIMSS-R Video Study of Mathematics and Science Teaching, the first author testified before a U. S. congressional committee on education. The testimony did not describe theories of creating SLOs, but it did outline the work we have described that lies behind the creation of these theories. The next day the first author received a call from a U.S. senator’s office asking for more details about such a plan for American schools. The senator’s assistant asked how long this would take. When the assistant was told 15 years, maybe 10 at best, he laughed and asked what a 1–2 year plan would look like. When he was told there was no such plan, he hung up the phone and was not heard from again. Educational theorists and researchers face major challenges in convincing themselves and others of the benefits of long-term research agendas.

6 Our Answers to the Editors’ Questions for the Authors

The editors of this book asked all authors to address the following questions, either in the context of their presentation or as an additional section at the end of their chapter. We have addressed most of the questions but our answers might be somewhat hidden and implicit. So, we will address all four questions here. If the earlier sections contained relevant responses, our answers will be brief.

6.1 What Is a Theory (of Teaching)?

We can begin with the definition of theory that we presented and that is consistent with the definition presented in the introductory chapter by the editors of this volume (Praetorius & Charalambous, this volume): an interrelated set of ideas intended to explain something. The statement we borrowed from Hill and Smith (2005)—“theory helps identify what factors should be studied and how and why they are related”—helps to clarify our focus. Because we are interested in theories of teaching that teachers actually can use, our theories of teaching attended to “factors” of the classroom environment that teachers normally use to make instructional decisions.

This bias toward theories that are usable by teachers leads us to the following answer to this first question. In a general sense, theories of teaching must account for how the intended curriculum, broadly defined, is transformed into learning opportunities that are experienced by students. This means that, in our view, theories of teaching consist of connected sets of hypotheses that predict how specific instructional activities and tasks will produce learning opportunities experienced by students in particular ways. That is, theories of teaching are capable of guiding the cause-effect reasoning that lies at the core of making instructional decisions about what kinds of tasks and activities will yield what kinds of sustained learning opportunities, and they do so with an eye toward studying and improving these decisions.

6.2 Can Such a Theory Accommodate Differences Across Subject Matters and Student Populations Taught? If So, How? If Not, Why?

Our response is “yes,” and “no.” Theories of teaching can be developed in general ways that allow researchers and educators to swap out subject matter, student populations, and other contextual variables without changing the theory. Returning to our interest in theories that are useful for teachers, such theories could help teachers make and test instructional decisions but mostly in general and vague ways. More helpful theories would be those developed with more specificity, and more specificity requires building into the theories information about contextual variables.

For example, when Lucy Scott, our sixth-grade teacher, makes decisions about what tasks could help her students understand equivalent fractions and how to implement these tasks, a useful theory would contain informed hypotheses about the kinds of experiences students need to develop conceptual understanding of key mathematical concepts and how to create them. The more specific the hypotheses are about developing understanding of equivalent fractions, the more useful the theory. The hypotheses would specify features of these experiences, like struggle-first, that would, in turn, suggest selecting equivalent fraction tasks with considerable cognitive demand and situating them deliberately in lessons so as to increase her students’ chances of experiencing productive struggle with equivalent fractions. Theories would become increasingly useful as other teachers experimented with similar tasks and researchers accumulated information over multiple trials.

This leads to another element of theories of teaching that makes them useful for teachers: hypotheses are specific enough to be indexed according to the learning goals or outcomes students are asked to achieve. Because different classroom experiences are related to different learning outcomes, teachers will want to access hypotheses about the kinds of teaching actions that will lead to experiences aligned with the learning goals they want their students to achieve. If the hypotheses are too general, they cannot help teachers like Ms. Scott make instructional decisions for this lesson with this learning goal.

6.3 Do We Already Have a Theory/Theories on Teaching? If So, Which Are They?

This question is difficult to answer because, in our view, theories of teaching are necessarily so complex that they are only in progress; they are never complete. In our view, not shared fully with some authors in this volume, the status of a theory can be measured by the number of hypotheses that have been formulated, the range of classroom learning events they can predict, and the state of empirical confirmation of these predictions. Using these criteria, we would say the field has theories at the very beginning stages of development. Often, the “theories” are more like small collections of hypotheses that still need to be fully tested.

One of the huge challenges facing theorists of teaching became clear for us while working on the TIMSS video studies. We learned that, although it is possible within a single culture to maintain the view that teachers’ particular actions are the causes of particular learning outcomes, this view is hard to sustain in the context of cross-cultural comparisons. We found that many of the variables educators have believed are important—whether teachers lecture to the whole class or divide the class into student work groups, whether teachers use concrete or abstract representations, whether teachers use technological tools or just write on the chalkboard—turn out to vary among these countries. These do not appear to warrant theorists’ attention as individual variables. It was not the teachers’ actions, or even the problems presented to students, that higher-achieving countries shared. Rather, it was how the elements of a lesson were configured and the way in which students engaged with the learning opportunities.

To make things even more challenging, we found that different kinds of teacher actions could produce similar kinds of learning opportunities and similar kinds of teacher actions could produce different learning opportunities. What mattered was the way in which students took up the opportunities. Across the higher achieving countries, we saw many different instructional strategies and teachers’ actions that resulted in the richest kinds of learning opportunities—repeated opportunities for students to engage in productive struggle to make connections among important mathematical concepts, facts, and procedures. These findings help to explain why the field is struggling to build theories of teaching that teachers can use.

6.4 In the Future, in What Ways Might It Be Possible, If at All, to Create a (More Comprehensive) Theory of Teaching?

Our first response to this question is that we have described what Lipsey (1993) calls “small theories attempting to explain treatment processes, not a large theory of general … phenomena” (p. 11). In this sense, we have shown, at least implicitly, our bias against “comprehensive” theories of teaching. This is due partly to our belief that “small theories,” focused on teaching processes that lead to particular learning opportunities for students, are the kinds of theories that will be useful for teachers. Our interest in “small theories” also is due to our skepticism that, at this point in the history of theory development and research on teaching, developing a comprehensive theory of teaching is likely, or is even the next best step.

However, we certainly endorse the goal of creating more comprehensive “small theories.” Our answer to the question of creating gradually more comprehensive (small) theories is contained in our descriptions of building theories of creating sustained learning opportunities. We can pull out a few features of this work that seem especially important: begin with documented connections between the kinds of sustained learning opportunities that yield specifiable learning outcomes; develop hypotheses about how teachers can create sustained learning opportunities of the targeted kinds; continuously test and revise predictions suggested by the hypotheses; coordinate the work of teachers and researchers to test predictions and revise hypotheses; aggregate findings across classrooms and search for patterns that rise above specific contexts; and, find ways to create sustainable partnerships between teachers and researchers, and build networks of partnerships. As learning theorists and researchers continue to identify the features of sustained learning opportunities that yield particular learning outcomes, researchers and teachers can continue to expand the scope of their theories of teaching.

We want to repeat that the processes we have identified for building more comprehensive theories are tailored to the values we expressed at the beginning of the chapter and to the kind of theories in which we are most interested. Stepping back, we recognize that the processes for building theories of teaching will result, in large part, from the kinds of theories the community wishes to build. Authors of other chapters in this volume outline different theory-building agendas.