Theory and Research on Tasks Revisited: Task as a Context for Students’ Thinking in the Era of Ambitious Reforms in Mathematics and Science

What Is a Task?

As Doyle (1988) stated, the “multiplicity of meanings [of the term task] complicates task research. At the same time, the richness of the term contributes to its productivity and suggests that it captures an important part of classroom life” (p. 170). When we use the word task in this essay, we refer to any instructional or assessment-related unit of disciplinary work that is assigned to students to intellectually engage them in science or mathematics. Specifically, we define a task as a segment of a classroom activity devoted to the development and assessment of a disciplinary idea and/or a practice (Stein, Smith, Henningsen, & Silver, 2009; Tekkumru-Kisa, Stein, & Schunn, 2015). In short, a task creates the context within which students think about the subject matter (Doyle, Sanford, Schmidt-French, Clements, & Emmer, 1985); as such, it can provide researchers and practitioners with an analytical framework to define and explain the nature of students’ intellectual work.

An important feature of tasks is that they can exist at multiple levels: (a) the task as designed (e.g., as it appears in written materials) characterizes the potential level and kind of thinking in which students are invited to engage; (b) the task as set-up by the teacher characterizes the framing of the intellectual work for the students (i.e., the level and kind of mathematical or scientific thinking they are expected to engage in); (c) 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) (Doyle, 1988; Smith & Stein, 1998; Tekkumru-Kisa, Schunn, Stein, & Reynolds, 2019; see Figure 1); and (d) the task as assessed characterizes the intellectual products that students are held accountable for knowing (Doyle, 1988), using, and making sense of. Therefore, as tasks come to life in classroom interactions, they can be viewed as “in motion” in relation to the level and kind of student thinking.

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Figure 1.

The task framework.

Why Focus on Tasks Now?

There are several reasons to revisit theory and research on tasks in today’s educational climate. First, tasks are recognizable and consequential units of analysis in the development and implementation of curriculum, instruction, and assessment (Tekkumru-Kisa et al., 2015), all of which are key channels to communicate the vision of instructional reforms. The recent state-led policies have specified an ambitious vision of teaching and learning in science and mathematics and “channels of influence” through which that vision can be brought to classrooms (National Research Council, 2001). These channels include curriculum, instruction, assessment, and professional development. Reformers’ theory of action is that aligned messages will flow through these channels, hopefully unaltered, to teachers who will reconfigure their instruction in ways that will provide students with the opportunity to learn as espoused in the ambitious reforms.

Tasks exist at the optimal grain size for conveying the vision of reforms into classrooms because they meaningfully capture the ideas envisioned in today’s high-level policies. For example, assessments consist of tasks, and student proficiency can be assessed at the task level and evaluated in terms of its alignment to reform vision (e.g., Achieve, 2018). Curriculum is organized around tasks that are carefully sequenced to support developing students’ proficiency (e.g., Blumenfeld, Soloway, Marx, Krajcik, Guzdial, & Palincsar, 1991; Tekkumru-Kisa & Schunn, 2019). Similarly, instruction can be understood when analyzed in a meaningful chunk such as the enactment of a particular task from beginning to end, thereby providing information not only about the task as designed but also about the quality of teaching and learning as viewed through the enactment of the task with the teacher and students (e.g., Boston, 2012; Tekkumru-Kisa, Preston, Kisa, Oz, & Morgan, 2019). Tasks have also been used to support pre- and in-service teachers’ learning to develop ambitious teaching practices (e.g., Arbaugh & Brown, 2005; Boston & Smith, 2009; Johnson, Severance, Penuel & Leary, 2016; Mason & Johnston-Wilder, 2004; Ross & Cartier, 2015; Tekkumru-Kisa, Stein, & Coker, 2018). Focusing on tasks within each of the channels of influence allows researchers to see, organize, and analyze students’ opportunities to learn in meaningful ways. Therefore, when used as a common unit of analysis across channels, tasks can support researchers’ comparisons among students’ opportunities to learn in classrooms, what they learn, and the vision espoused by the ambitious reforms called for by state- and district-level policies.

Second, tasks are important because they constitute a common classroom-based element between the work of the teacher and the work of students. For most of the 1970s and 1980s, researchers focused on either student learning or teacher behavior in the classroom. There was little in the way of a “unified paradigm” for studying what teachers thought about or did in the classroom and what or how students learned (Fennema, Carpenter, & Lamon, 1991, p. i). Research on tasks served as a bridge between these two bodies of work. Most important, it helped us understand the mechanism through which teaching affects student learning. We now know that tasks set the parameters for “what is possible” in terms of the kinds of thinking students might engage in; consequently, selecting, designing, and modifying tasks for teaching is recognized as an important aspect of teaching. This was not always the case. Prior to the 1990s, researchers on teaching focused on teacher characteristics (e.g., a warm demeanor) or general teaching practices (e.g., wait time). In the late 1980s, research on teaching began to attend to the teaching of subject matter (Shulman, 1986). An underlying premise of the subject matter–specific work has been the focus on the logic of learning (i.e., how students learn science or math). This “logic of learning,” in turn, is set into motion by the kinds of work the teacher sets before students get in the classroom (i.e., the “tasks”). Therefore, tasks and their teacher-guided facilitation shape what students attend to, how they process information, what skills they practice, what disciplinary practices they engage in, and, most important, what they learn (e.g., Sanford, 1987).

Third, the focus on tasks helps us understand how to support attention to student thinking. Contemporary conceptual models such as teacher noticing (Sherin, Jacobs, & Philipp, 2011), ambitious science teaching (Windschitl, Thompson, Braaten, & Stroupe, 2012), and responsive teaching (Robertson, Scherr, & Hammer, 2015) emphasize the importance of attending to students’ ideas for effective teaching and learning. Rightly so, students’ ideas are emphasized as important resources to facilitate learning while planning for and enacting rigorous instruction. At the same time, there has been a growing emphasis in supporting pre- and in-service teachers’ learning to be responsive to students’ ideas in professional development programs and teacher preparation (e.g., Jacobs, Lamb, & Philipp, 2010; Levin, Hammer, & Coffey, 2009; van Es & Sherin, 2006). Missing from this literature and professional learning programs derived from it, however, is any attention to tasks. Not attending to tasks can lead researchers to ignore the context for students’ thinking and consideration of how to create opportunities to elicit student thinking, which can then be noticed by the teacher. Given that tasks serve as “a context for students’ thinking” (Doyle, 1988, p. 167) and that different tasks elicit different kinds and levels of student thinking, teachers’ opportunities to attend to student thinking would differ on the basis of the kind of tasks in which students are engaging.

Finally, the work on tasks sits at the boundary of research and practice. Ambitious instructional reforms have brought with them the importance of long-term partnerships between researchers and practitioners. Recently, there has been a growing emphasis on research–practice partnerships that are organized to investigate and address problems of practice for improving education systems (Penuel & Gallagher, 2017). In these partnerships, tools and routines are important for building an infrastructure that supports collaborations by building a common language and sets of practices. Tasks can serve as a common unit across researchers and practitioners for describing the kind of intellectual work in which students are expected to and do engage in: Teachers, for instance, think about and use tasks in their daily practice and would easily engage in productive discussions with researchers about the tasks they use in terms of their potential for students’ thinking. Similarly, analyzing the tasks that are assigned to students in the classroom provides an analytical lens to researchers for understanding teaching and students’ opportunities to learn. Moreover, analyzing and modifying tasks, and thinking about ways to effectively implement them, have been the focus of many teacher preparation and professional development programs, so tasks, again, serve as a common practical tool across teacher educators, pre- and in-service teachers, and researchers (e.g., Boston & Smith, 2011; Johnson et al., 2016; Tekkumru-Kisa et al., 2018). We believe that tasks’ sitting in this boundary of research and practice where they are commonly used by researchers and practitioners is advantageous for building partnerships. This natural overlap can facilitate the development of a common language and organically grow sustainable efforts that address problems of practice emerging from real needs and motivations.

All of this suggests that tasks will continue to play a significant role in mathematics and science education, whether or not they are also the focus of research. To unpack these issues further in relation to the existing knowledge base in these fields, we turn to a brief theoretical and empirical synthesis of the early research on tasks conducted by Doyle and colleagues. We then discuss how this research on tasks has been taken up and expanded in mathematics and science education through the development of tools and frameworks as well as the design of learning environments for teachers that systematize, operationalize, and communicate the major insights associated with tasks in research and practice. We close by discussing areas for future research and development to improve the quality of teaching and learning experienced by students as envisioned by the current ambitious instructional reforms.

Foundational Research on Tasks

In the early 1980s, Walter Doyle led a large project that focused on the nature of academic work in secondary classes in several subject areas. The Managing Academic Tasks (MAT) study built an important foundation for research on tasks in science and mathematics education. Phase I of the MAT study investigated academic tasks in junior high school classes in science, mathematics, social studies, and English. Phase II of the study focused on academic tasks in senior high school science and English classes (Doyle et al., 1985). In this work, the cognitive demand of a task was identified on the basis of the cognitive processes students use to accomplish it. Doyle and colleagues categorized tasks across different content areas as higher order (or at a comprehension level) when students were not required to complete the task by (a) simple memory, (b) routinely or automatically applying an algorithm, or (c) search and match (i.e., finding the answer by matching similar elements and copying) (Doyle, 1983; Doyle et al., 1985; Sanford, 1987).

This foundational work on tasks produced consistent findings across the content areas. High-level tasks were less frequently used, and implementing them well was hard for teachers and stressful for students. Students often perceived these tasks as highly ambiguous (i.e., not having a predictable pathway for approaching them) and/or risky (i.e., having a low likelihood of completing the task successfully) (Doyle, 1983; Sanford, 1987). This early research also revealed the important role of the teacher in selecting and managing high-level tasks. Doyle et al. (1985) argued that teachers affect students’ learning by defining the tasks students are to accomplish and by managing their interactions with students around the task. The research also identified several factors that influenced how well teachers managed the implementation of high-level tasks in their interactions with students, such as checking on only procedures and completion (e.g., Doyle & Sanford, 1985; Sanford, 1987).

Research on Tasks in Mathematics Education

The introduction of the Curriculum and Evaluation Standards for School Mathematics in 1989 represented a watershed moment in mathematics education. These standards persuasively argued that students were spending too much time working on routine problems by applying a known procedure and not enough time working on nonroutine, unstructured problems that required them to learn how to think, reason, and solve problems using disciplinary practices. Initially, a critical problem was teachers’ lack of access to high-level, “doing mathematics” tasks because the vast majority of commercial curricula featured low-level, procedural tasks (Stein, Remillard, & Smith, 2007). However, after teachers were provided with better materials (a rash of curricular materials were developed in the mid- to late 1990s), a second problem arose: maintaining the potential of the task through its introduction to students and its enactment once students started working on it. Decreasing the distance between the potential of a task and how students were actually thinking as they were engaged with the task became a consistent theme within mathematics education for at least two decades, with “maintenance of cognitive demand” often viewed as the sign of a successful lesson.

Framing instruction in this way owes a clear debt to the earlier work of Doyle and his colleagues. Mathematics educators extended Doyle’s work through the further specification of the kinds of thinking and reasoning that high-level mathematics tasks should elicit and with the development of frameworks and tools that have been widely adopted and adapted throughout the mathematics education community. For example, Stein et al. (2009) identified and classified the variety of task-based cognitive processes into two general levels, each of which was further subdivided (plus one). ¹ The Mathematical Task Analysis Guide (TAG; Figure 2) has been used to analyze the cognitive demand of mathematical tasks in scores of research articles and hundreds of professional development sessions. The TAG also forms the basis of several practitioner articles (e.g., Caulfield, Harkness, & Riley, 2003; Lambert & Stylianou, 2013) and best-selling books (Stein et al., 2009; Smith & Stein, 2011).

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Figure 2.

Task analysis guide.

Another task-based tool that proved to be useful was the Task Framework (Figure 1), which draws attention to the potential for the decline of cognitive demand across the phases of a task. Research in mathematics education also revealed that particular patterns of decline could be identified along with classroom-based factors that often accompanied such declines such as routinizing problematic aspects of a task (Henningsen & Stein, 1997; Stein, Grover, & Henningsen, 1996; Stein et al., 2009). Lists of factors associated with maintenance and decline of high-level tasks have also proved useful to both researchers and practitioners. Finally, the aforementioned task-centric research and development would not have been as prolific as it was without research showing that maintaining cognitive demand was associated with students’ gains on an assessment of thinking, reasoning, and problem solving (Stein & Lane, 1996).

Research on Tasks in Science Education

Since the release of the Framework for K–12 Science Education (National Research Council, 2012) and the NGSS (NGSS Lead States, 2013), science education in the United States has been going through rapid and significant changes in curriculum, assessment, and instruction. By bringing attention to the exclusive focus on science content (i.e., the established body of scientific knowledge) independent of the scientific practices in many science classrooms, the National Research Council (2012) underscored that “Learning science . . . involves the integration of the knowledge of scientific explanations (i.e., content knowledge) and the practices needed to engage in scientific inquiry” (p. 11). Focusing on scientific practices is meant to engage students in sensible versions of the actual intellectual work that scientists engage in (Bell, Bricker, Tzou, Lee, & Van Horne, 2012). Students’ grasp of how and when to use practices to explain phenomena has become more critical with this “practice turn” in science education (Ford, 2015; Furtak & Penuel, 2018). Rather than simply presenting students with facts and definitions as ends in themselves, it became important to help students work toward developing explanatory models from evidence (Lehrer & Schauble, 2006; National Research Council, 2015).

In the report by the National Research Council (2015) that was released as a guide to implementing NGSS-like standards, it was emphasized that

The types of tasks that students are asked to engage in will look different in a classroom aligned to the NGSS. . . . Tasks teachers have typically assigned to students—either in class, for homework, or for assessment purposes—need to be carefully reconsidered in light of the learning goals of the Framework and the NGSS. (p. 34)

The question, then, is, What are the features of science instructional tasks at different cognitive demand levels that can (or cannot) engage students in the kinds of learning opportunities envisioned in the framework? Addressing this question, Tekkumru-Kisa et al. (2015) developed the Task Analysis Guide in Science (TAGS; Figure 3). Informed by the National Research Council framework, the TAG, and research on cognitive demand and how students learn science, the TAGS is a two-dimensional framework that differentiates science tasks by considering both cognitive demand and the integration or isolation of science content and scientific practices. Crossing these two dimensions yields nine different categories that distinguish science tasks on the basis of the level and kind of thinking they require and if and how students are expected to engage in scientific practices.

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Figure 3.

Task analysis guide in science.

The TAGS allows analytical and refined analysis of the intellectual work demanded of students in science classrooms. In the earlier research on tasks, science tasks were categorized as high level when they required more than memory, routine application of an algorithm, or a simple search and match strategy (Sanford, 1987). According to the TAGS, high-level tasks require the use of scientific ideas and a “grasp of practice” (Ford, 2015). They are often ambiguous without a clear pathway to follow and may involve some level of anxiety for students because of the unpredictable nature of the process (Tekkumru-Kisa, Schunn, & Stein, in press; Tekkumru-Kisa et al., 2015). Thus, they provide robust opportunities for students to engage with uncertainty as experienced in nonobvious and contingent aspects of scientists’ work (e.g., Chen, Benus, & Hernandez, 2019; Engle, 2012; Manz & Suárez, 2018). Engaging students in scientific practices can help develop their understanding of “how that practice contributes to how we know what we know, and how that practice helps to build reliable knowledge” (Osborne, 2014, p. 189). Therefore, the TAGS requires attention to students’ intellectual engagement in “not only the content of science—facts and concepts, for example—but also the doing of science—the habits of mind, skills, and practices that bring science to life” (National Academies of Sciences, Engineering, and Medicine, 2015, p. 28).

Undoubtedly, teachers play a critical role in shaping students’ opportunities for learning through the tasks that they select. Teachers, however, often have different views of what makes a science task cognitively demanding for students. For example, in a recent study, the majority of the tasks teachers identified as cognitively demanding were classified by researchers using the TAGS as low level (Tekkumru-Kisa, Kisa, & Hiester, 2020). Consistent with prior research, research in science education has also indicated that even when teachers select high-level tasks, the cognitive demand of those tasks often declines during their implementation (Kang, Windschitl, Stroupe, & Thompson, 2016; Tekkumru-Kisa, Schunn, et al., 2019); intellectually rich activities have a history of being proceduralized in science classrooms (Roth & Garnier, 2007; Weiss, Pasley, Smith, Banilower, & Heck, 2003). The Task Framework shown in Figure 1 has informed the field in science education to identify and describe the changes observed in students’ thinking across the phases of a task (e.g., Kang et al., 2016; Tekkumru-Kisa, Schunn, et al., 2019). It helped reveal instructional factors that play a role in maintaining students’ high-level thinking during students’ engagement in cognitively demanding tasks, including attending to and advancing students’ ideas and pressing for sensemaking (Tekkumru-Kisa et al., 2018; Tekkumru-Kisa, Schunn, et al., 2019).

Promoting the Selection and Implementation of Cognitively Demanding Tasks

In most science and mathematics classrooms today, the tasks students are asked to do consist of typical labs or problems with routine pathways to complete (Hofstein & Lunetta, 2004; National Research Council, 2015; Weiss et al., 2003). These tasks provide students opportunities to learn “school math” or “school science,” not the processes of mathematical or scientific thinking. Moreover, the goal—at least in terms of students’ perspectives—is to complete the worksheets as quickly as possible. In short, many of today’s tasks do not provide students with the kinds of opportunities to learn demanded by the new generation of standards. Many science lessons, for instance, tend to portray science as a static body of knowledge with limited opportunities for engaging students in doing science (Banilower, Smith, Malzahn, Plumley, Gordon, & Hayes, 2018; National Research Council, 2012; Weiss et al., 2003). When teachers use hands-on activities, they often neglect to make connections to core science ideas (Hofstein & Lunetta, 2004; Roth, 2014). Similarly, in mathematics, teachers may embrace students’ use of manipulatives, but close observation of students’ working on tasks using pattern blocks or fraction strips reveals little contact with the mathematical logic or ideas contained in the task (Cohen, 1990; Minor, Desimone, Lee, & Hochberg, 2016; Spillane, 2000; Spillane & Zeuli, 1999). Professional development and teacher education programs—combined with high-quality curriculum materials and aligned student assessments—can provide the support needed to change this state of affairs.

The TAG and the TAGS have been used in professional development and teacher education programs, and research has provided evidence for the effectiveness of these programs (e.g., Arbaugh & Brown, 2005; Boston & Smith, 2011). For example, learning to differentiate between mathematics instructional tasks on the basis of cognitive demand increased teachers’ focus on student thinking and resulted in changes in their instructional practices (Boston, 2012). Although research in science education has not been as rich in how to support teachers’ learning to differentiate between science tasks, a recent report (Banilower et al., 2018) indicates why this would be necessary for science teachers’ professional development. According to a national survey of science teachers, teacher-created lessons heavily influence instruction in science classrooms regardless of whether instructional and curricular materials are provided to the teachers. In more than 75% of secondary school science classrooms, teacher-created lessons form the basis of science instruction (Banilower et al., 2018), indicating the pivotal role of science teachers in the selection of instructional tasks for students’ engagement in science classrooms (Tekkumru-Kisa et al., 2020). Therefore, more research is needed that identifies how to support teachers’ learning to design lessons structured around cognitively demanding science tasks. For example, recently, Kloser (2017) suggested that professional learning communities would benefit from analyzing science tasks on the basis of their cognitive demand levels to effectively engage students in science investigations in the classrooms. Teachers can undoubtedly benefit from professional learning communities and other forms of professional learning opportunities designed to promote the use of cognitively demanding tasks in science and mathematics classrooms.

Teachers also need to learn how to support the enactment of cognitively demanding tasks. Prior work on tasks has demonstrated that teachers and professional developers resonate with the idea of tasks, especially to the finding that tasks’ thinking demands can change as they “progress” from textbook and curricular materials, through classroom setup, to enactment with the students as presented in the Task Framework (see Figure 1). Often the change represents a decline in which the teacher may be implicated, thereby leading to an opportunity for focused professional development. Instructional factors associated with maintenance and decline of cognitive demand on students’ thinking across these phases are used to support teachers’ learning in professional development and teacher preparation programs.

Tasks and their implementation, as demonstrated through artifacts of practice, have been used to support teachers’ learning. The Problem-Solving Cycle, a research-based professional development model (Koellner et al., 2007; Borko, Jacobs, Eiteljorg, & Pittman, 2008), is an example from mathematics. The model consists of three workshops organized around a rich mathematical task (Borko, Jacobs, Koellner, & Swackhamer, 2015), around which teachers develop lesson plans. Teachers teach the focal tasks in their classrooms and in follow-up professional development sessions, watch video clips of one another’s instruction, and review student work collected from the lesson. Teachers explore students’ thinking and the teacher’s role by focusing on issues such as launching the task and orchestrating classroom discourse (Borko et al., 2008). Similarly, Teaching Science With Cognitive Demand, a video-based professional development, was designed to support science teachers’ learning to select and effectively implement cognitively demanding science tasks that promote student engagement in high-level thinking and sense-making (Tekkumru-Kisa & Stein, 2017). By using the power of video in facilitating teachers’ learning (Brophy, 2004; Sherin, 2004), Teaching Science With Cognitive Demand involved teachers’ analyzing video clips that depicted the enactment of cognitively demanding tasks in science classrooms, including videos from teachers’ own classrooms and from their colleagues’ classrooms and the contrasting video cases of maintenance and decline (Tekkumru-Kisa & Stein, 2014, 2015).

Summary

The idea that “all tasks are not created equal” (Doyle, 1983; Hiebert & Wearne, 1993; Stein et al., 1996; Tekkumru-Kisa et al., 2015) has informed how we think about science and mathematics education both theoretically and practically. Across the past 35 years of research on tasks, there are consistent patterns and important takeaways that shed light on supporting the ambitious goals of recent reforms. First, teachers are the key players in determining the learning opportunities experienced by students through the tasks they assign to students. Second, tasks pass through phases: tasks as they appear in written materials, tasks as launched by the teacher to frame students’ intellectual work, tasks as they enacted by the teacher and students in an activity system of complex classroom settings, and tasks as assessed. Demand on students’ thinking can change across these phases depending on the interaction between the students, the teacher, the content, and the classroom environment. Third, implementing cognitively demanding tasks is not easy both for students and the teacher. Teachers need professional development opportunities to learn how to facilitate students’ sensemaking and productive classroom interactions and discourse as students are working on these complex tasks. Similarly, students need consistent and supported experiences over time in working with cognitively demanding tasks so that such tasks become the norm for doing mathematics and science in classrooms.

Current work is indebted to Doyle and his colleagues’ identification of the importance of tasks and the challenges high-level tasks present to classroom teaching and learning. Mathematics and science educators have “moved the ball forward” by not only identifying the tendency of the cognitive demand of mathematics and science tasks to decline but also identifying reasons for that decline that sit mostly within the teachers’ control. Using tools and frameworks derived from research on tasks, mathematics and science educators have been able to (a) make teachers aware of the potential for the decline and (b) provide teachers with moves they can undertake to keep the intellectual work at a high level. Many studies of teacher learning to facilitate student thinking through cognitively demanding tasks have provided evidence for the effectiveness of these tools and frameworks. They have provided tangible actions for improvement and a common language across key stakeholders in research, policy, and practice.