DOK Alignment Tool for Math Teachers
Math assessments are especially prone to DOK 1 overload, pages of procedural practice that test whether students can execute an algorithm without testing whether they understand why it works. The DOK Alignment Tool gives a sheet for sorting every math item by Webb's Depth of Knowledge level, and you can read its levels for math as: DOK 1 (recall a formula or execute a routine procedure), DOK 2 (interpret a graph, apply a concept to a new problem type), DOK 3 (reason about a non-routine problem, explain mathematical relationships), DOK 4 (design a multi-step solution to a real-world problem). CCSS-aligned.
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How teachers use this for math teachers
Algebra I unit test audit
Classify solving-equations items by DOK level to confirm students must reason through multi-step problems, not just execute procedures they have memorized from homework.
Geometry proof assessment
Evaluate proof and justification questions by DOK level, logical reasoning in proofs is typically DOK 3, but some proof items can be DOK 1 if students are reproducing a memorized proof.
Pre-calculus function assessment
Check that function analysis questions require students to reason about domain, range, and transformation relationships (DOK 2-3), not just evaluate at a given point (DOK 1).
Statistics unit assessment
Audit data analysis questions to confirm students must interpret results and draw conclusions (DOK 3) rather than just calculate mean, median, and mode from a table (DOK 1-2).
Calculus free-response alignment
Compare classroom calculus items to AP Calculus free-response cognitive demands to ensure students are practicing the reasoning required on exam day.
Math department common assessment
Use the DOK counts to align cognitive demand expectations across all sections of the same course, supporting consistent rigor when multiple teachers teach the same unit.
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What this page does here
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Questions teachers ask
What does DOK 1 look like in math versus DOK 3?
DOK 1 in math: recall a formula, execute a memorized procedure on a routine problem (solve 2x + 5 = 13). DOK 2: interpret a visual representation, apply a procedure to a new context, identify the relevant operation in a word problem. DOK 3: reason about a non-routine problem, explain why an algorithm works, construct a mathematical argument, or design a solution strategy for a multi-step problem with multiple valid approaches.
Is procedural practice bad? Should all math assessment be DOK 3?
No. Procedural fluency at DOK 1 and 2 is essential, students cannot reason about mathematics if they cannot execute procedures accurately. The problem is not that teachers assess procedures; it is that many assessments stop there. A well-designed math assessment includes both procedural items and reasoning items. The sheet helps teachers see when the balance has tipped too far toward procedure at the expense of reasoning.
How does DOK relate to the CCSS Standards for Mathematical Practice?
The CCSS Standards for Mathematical Practice (make sense of problems, reason abstractly, construct viable arguments, model with mathematics) describe cognitive habits that operate at DOK 2-4. A math assessment that only assesses at DOK 1 does not assess whether students have developed the mathematical practices the standards require. The DOK sheet helps teachers ask whether their assessments actually assess the practices they are teaching.
Can I use this tool to audit a full math textbook's assessment bank?
Yes. Paste items from a textbook test bank into the form, then count them by DOK level on the sheet. Many commercially published math assessments lean toward DOK 1. Knowing this helps teachers select, supplement, or revise items from the bank to achieve a better distribution before administering a test.
What is a DOK 4 task in math?
DOK 4 tasks in math require extended thinking over multiple class periods, designing an original mathematical model, completing a multi-phase investigation, or producing a project that requires synthesizing multiple mathematical concepts to solve a complex real-world problem. These are typically project or performance task formats, not individual test questions. The sheet helps teachers sort these tasks just as it does for individual items.
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