Question: What is the 37th digit in the number pi? (No calculator or googling allowed!)
Coming up with the 37th digit of pi is a very difficult task. But it’s not a complex task. In our classrooms, it’s important that we know what makes a task complex versus difficult so that we can effectively address the rigor or depth of K–12 academic expectations. One of us (Norman Webb) developed the Depth of Knowledge (DOK) framework in the late 1990s precisely for this purpose: to categorize expectations and tasks according to the complexity of engagement required.
DOK provides a common language that can be used to determine the degree to which the complexity of cognitive engagement, explicit in academic standards, is being translated into appropriate learning opportunities and assessment tasks. Because today’s academic standards emphasize conceptual understanding and authentic application of disciplinary practice, evaluating complexity of engagement is more important than ever. This article explores how teachers and administrators can use DOK to work more efficiently, effectively, and purposefully when they design curriculum.
DOK IN THE CLASSROOM
In general, lessons and courses are anchored in academic standards. Even for coursework that is not standards-based, teachers design curriculum based on learning objectives. To use DOK in your practice, start by looking at the standards (or other learning objectives) that anchor a lesson. What is the complexity of cognitive engagement required for success? When interpreting a standard, you can use the full DOK definitions for a specific content area. These general key questions can also help:
DOK 1: Is the focus on recall of facts or reproduction of taught processes?
DOK 2: Is the focus on relationships between concepts and ideas or using underlying conceptual understanding?
DOK 3: Is the focus on abstract inference or reasoning, nonroutine problem-solving, or authentic evaluative or argumentative processes that can be completed in one sitting?
DOK 4: Is the focus at least with the complexity of DOK 3, but iterative, reflective work and extended time are necessary for completion?
Evaluating the complexity of an expectation or task. When using DOK to evaluate educational materials, think about the degree of processing of concepts and skills required. For example, recalling the names of the state capitals is a low-complexity task. Retrieving bits of information from memory requires a minimal degree of processing of concepts. Either it’s in there and can be accessed… or it’s not. Similarly, correctly executing a multistep protocol is a simple task: There are specific steps to follow, and the protocol is either completed correctly… or not. As another example, we may ask students to use the standard algorithm to add two three-digit numbers or to follow specific, ordered steps to properly focus a microscope.
In contrast, tasks that require abstract reasoning and nonroutine problem-solving are highly complex. For example, tasks that involve analyzing multiple alternative solutions with consideration of constraints and trade-offs or building original evidential arguments require significantly more processing of concepts and skills than do tasks that must be completed via recall.
For example, we may ask students to develop an engineering design solution to a problem they identify. We could have students write or present a research-based argument about what time school should start and end, taking into account different perspectives of students, families, and staff. Overall, complexity of cognitive engagement depends on multiple factors, including the degree of processing required, the degree of intricacies (interconnected parts), and the extent to which the work is concrete versus abstract.
Appropriate use of DOK differentiates difficulty from complexity. Although complex tasks (like analyzing alternative solutions or building an evidential argument) are likely to be difficult, many difficult tasks (like correctly following a multistep protocol or memorizing state capitals) are not complex. Overall, difficulty depends on multiple factors, including the amount of effort required, the opportunity for error, and the opportunity to learn. “What does a fossa eat?” is a very simple question. But for someone who has never had the opportunity to learn what a fossa eats, it is also a very difficult question—unanswerable, in fact.
Use of DOK can help ensure that tasks that are intended to be complex are, indeed, complex (and not just difficult). It is also important to recognize when difficulty is inherent to a task. For example, long division and use of standard English punctuation may be difficult, but they are also tasks that students are typically expected to master.
AVOIDING MISINTERPRETATIONS OF DOK
As DOK has become a widely used tool in the United States and beyond, a variety of misinterpretations have inevitably emerged. For example, a frequently reproduced and highly misleading graphic (known to some as “the DOK wheel” and to others as the “wheel of misfortune”) attributes verbs to the different levels of DOK. This graphic suggests that a verb can be used to determine the complexity of engagement required by an expectation or task.
For instance, according to this graphic, the verb identify indicates a DOK 1. That could surely work in some cases—imagine having students “identify the circle in a group of shapes.” But now imagine having students “identify a strategy for addressing attendance issues using data from multiple sources.” Obviously, the complexity of these two tasks is significantly different despite using the same verb. To determine complexity, we need to look beyond the verb and consider the full scope of an expectation or task.
Another common misrepresentation is seen in progression or stair-step models that depict DOK as a hierarchy like Bloom’s or Maslow’s. But learning does not necessarily progress “up” from simple to complex. Consider mathematics: We often have students work conceptually with an idea before we introduce a more simple, rote approach. For example, we typically have students work with manipulables and form conceptual constructs of the idea of area before we introduce the equation l x w = a.
If you have ever used project-based learning (PBL), you have likely seen that a student may dive into work on a DOK 3 problem only to discover a simultaneous need for a DOK 1 task, like looking up a definition or taking a measurement. In fact, the use of a complex problem to motivate a need-to-know for lower-complexity goals is a core rationale for use of PBL.
Misrepresenting learning as progressing from simple to complex can be harmful if students who struggle with low-complexity tasks are held back from the rich, engaging, complex educational opportunities that we know promote learning. Ensuring access to complex learning opportunities for all students is foundational to the equity-focused goals of standards-based systems.
Incorporating DOK into practice can start by using the simple questions included here to ensure clearly and commonly understood learning targets. Then, the same process can be applied to the questions, tasks, and prompts we use in lessons and assessments. By defining and naming the DOK of the different components, we can work with greater focus and intentionality to check that the complexity of engagement explicit within those learning targets is carried through in the classroom.
And, by the way, the 37th digit of pi is 4.