Mathematics Depth of Knowledge levels

Our article on Depth of Knowledge delves into one of the most misunderstood rubric, and through this post, we aim to present a more extensive look into the Mathematics and Science Depth of Knowledge levels, while also presenting the most relevant verbs associated with each level. By the end of this post, “How does DoK assessment translate to the assessment of Maths and Science tasks?”, is the question we hope to answer.


DOK- Maths
Level 1 (Recall and Reproduction)

In mathematics, it can correspond to a one-step, clearly defined, and straight algorithmic procedure, or solving basic calculation problems that require a single step (addition, subtraction, Et al.). Keywords that signify Level 1 Depth of Knowledge in mathematics are: “Identify”, “recall”, “measure”, “recognize”, and “use”.


Level 2 (Skill/Concept)

This requires the student to make some decisions as to how to best approach the problem, and to contrast as well as compare concepts. “Estimate”, “organize”, “make observations”, “classify”, “compare data”, and “collect and display data” are keywords of this level.


Level 3 (Strategic Thinking)

The activities at this level typically require the student to explain their thinking as well as logic and make conjectures. “Explain and support with evidence”, “draw conclusions from the observations”, “explain the phenomena in terms of concepts”, and “cite the appropriate evidence and develop a logical argument for the concept”, represent the keywords for this Depth of Knowledge level.


Level 4 (Extended Thinking)

In the tasks of this level, the learner has to create multiple connections and relate within and among the applicable content areas in order to select the best approach to solve the problem. Following are the keywords of Level 4 Mathematics Depth of Knowledge: “Create and carry out experiments”, “combine and synthesize ideas into concepts”, and “critique the experimental design”.


Science Depth of Knowledge levels


In science, “knowledge” can refer to both, content knowledge as well as knowledge of processes.



Level 1. Recall and Reproduction

Simple science procedures/processes and a distinct series of steps are performed in Level 1 of Science Depth of Knowledge. Some examples that represent a few Level 1 tasks include:

  • Performing a routine procedure (measuring height).
  • Represent a scientific theory or relation in words or diagrams.
  • Recall or recognize a definition, theory, or property.


Level 2. Skill/Concept

Problems that contain keywords like “classify”, “estimate”, “organize”, “make observations”, Et al., which require multiple steps for solving are classified under this level. Example:

  • Organize, represent, and interpret the data.
  • Represent and explain the relationship between facts, terms, properties, or variables.
  • Describe and explain examples and non-examples of science concepts.


Level 3. Strategic Thinking

The solutions of tasks classified within this level require an explanation not only of the conclusion reached but of the thinking and reasons for choosing the appropriate answer. Few Level 3 tasks include: 

  • Developing a scientific model for a complex situation.
  • Solving non-routine problems.
  • Identify research queries and create investigations for a scientific problem.


Level 4. Extended Thinking

Tasks at this level are complicated and cognizance intensive. They require complex reasoning, experimental design, and planning, and may very well go on for an extended period of time. Its examples include:

  • Carry out an investigation, from stating a problem to creating and conducting an experiment, to analyzing its data and forming conclusions.
  • Based on the data from a unique, complicated experiment given to the student, deduct the fundamental relationship between several controlled variables.


For more information relating to Depth of Knowledge, refer to this comprehensive post at Teachthought and Webb’s original research paper.


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