Tackling Math DoK

While the vast majority of my assessment and curriculum experience is tied to English/Language Arts, I have had to tackle Mathematics when selecting items and editing assessments. As part of my review process I need to ensure that the pool of items includes a good distribution of assessment questions that address different levels of Depth of Knowledge (DoK). Let’s explore the hallmarks of Math DoK.

*Please also see my earlier post: “Depth of Knowledge (DoK) for Reading.”

Level 1

This is the level of recall and reproduction. For students taking on Level 1, work centers on math facts, definitions, terms, simple procedures, as well as performing a simple algorithm or applying a familiar formula.

Common verbs found in item stems will be along the lines of “identify,” “recall,” “recognize,” “use,” “compute,” and “measure.” The items and expectations will require students to compute a sum, difference, product, or quotients.

Even Simple word problems that can be directly translated into a number sentence and solved by computation are Level 1 items. Verbs such as “describe” and “explain” could be classified at different levels depending on what is to be described and explained.

Some examples of Level 1 performance include:

• Recall or recognize a fact, term, or property.
• Compute a sum, difference, product, or quotient.
• Represent in words, symbols, or pictures a mathematical object or relation.
• Provide or recognize a standard mathematical representation for a given situation.
• Provide or recognize equivalent representations.
• Perform a simple procedure such as a measuring the length of an object.

Level 2

At Level 2 students are engaging in some mental processing that goes beyond Level 1’s recalling or reproducing. A Level 2 item requires students to make some decisions as to how to approach the problem, while Level 1 requires students to demonstrate a rote response, perform a well‐known algorithm, follow a set list of directions (e.g., a recipe), or perform a clearly defined series of steps.

Common Level 2 verbs are: “classify,” “organize,” ”estimate,” “make observations,” “collect and display,” and “compare.” Level 2 items require more than one step. E.g., to compare data can require identifying, grouping, or ordering the objects.

Other Level 2 activities include making observations and collecting data; classifying, organizing, and comparing data; and organizing and entering data in tables, charts, and graphs.

Some examples of Level 2 performance include:

• Specify and explain the relationship between facts, terms, properties, or operations.
• Coordinate different representations depending on situation and purpose.
• Select a procedure according to specified criteria and perform it.
• Formulate a routine problem given data and conditions.
• Compare given strategies or procedures.
• Solve a routine problem that requires some interpretation with multiple steps/parts.
• Provide justification of one or more steps in a routine procedure.

Level 3

Level 3 items touch on strategic thinking. Level 3 items require reasoning, planning, utilizing evidence, and we see more critical thinking on display then we do in Level 1 and 2 items. Many items will require students to explain their thinking.

The cognitive demands at Level 3 can be complex and abstract. Items and tasks will ask students to draw conclusions from observations, cite evidence and develop a logical argument for concepts, and use concepts to solve non-routine problems.

Some examples of Level 3 performance include:

• Analyze similarities and differences between problem‐solving strategies.
• Formulate an original problem given a situation.
• Provide justification for the steps in a solution process.
• Solve non‐routine problems.
• Formulate a mathematical model for a complex situation.

Connecting Webb’s Depth of Knowledge to the Common Core and Technology-Enhanced Items

Webb is part of the Common Core State Standards Validation Committee and it’s helpful to think about how his DoK model can be used with the CCSS and Technology-Enhanced Items.

The Common Core State Standards for Mathematics call for key shifts that complement Math DoK by revolving around focus, coherence, and rigor. And each level I’ve described above (1-3) can be traversed with higher-order questions built by TEIs.

Perhaps one of the best ways to give students practice with real-world interactive assessment items—mastering each DoK Level and the Common Core—relies on the leveraging of TEIs. This also allows teachers to quickly measure the efficacy of their assessments. But I’ll let the question types speak for themselves.