Most “rigorous” math items aren’t rigorous — they’re long. The numbers get uglier, the steps multiply, and the thinking stays exactly where it was. If you want items that stretch students, the lever is the demand you place on reasoning, not the demand you place on their patience.
Here’s a working definition you can apply in the middle of a prep period.
The three levels, in classroom terms
DOK 1 — recall and routine procedure. The student knows what to do the moment they read it. Execute a known algorithm, recall a definition, read a value off a graph. “What is 3/4 of 20?” is DOK 1 whether the answer is 15 or 15.375.
DOK 2 — apply a concept, make a decision. The student has to choose an approach, organize information, or move between representations. There’s a small decision embedded before the procedure starts: which operation, which representation, what does this quantity mean here.
DOK 3 — reason, justify, and defend. The student has to construct an argument, evaluate someone else’s, or work backwards from a constraint. There is usually more than one defensible path, and the explanation is part of the answer.
If a student can start computing before they finish reading, you’ve written DOK 1.
That heuristic catches most misclassified items. DOK 2 and 3 items require a beat of thought before the pencil moves.
Four moves that raise DOK honestly
1. Hide the operation, not the numbers
DOK 1: A recipe uses 3 cups of water for every 1 cup of concentrate. How much concentrate for 12 cups of water?
DOK 2: Two pitchers are labeled below. One uses 3 cups of water per cup of concentrate; the other uses 5 cups of water for 2 cups of concentrate. Which pitcher tastes stronger?
Same arithmetic weight. The second requires the student to decide that “stronger” means comparing ratios, and to pick a comparison strategy. The decision is the rigor.
2. Ask for the reasoning, not the result
DOK 3: Marisol says the 5-to-2 pitcher is stronger because 5 is bigger than 3. Explain what Marisol is comparing, and what she should compare instead.
Critiquing a flawed argument is the cheapest reliable route to DOK 3, and it doubles as diagnostic gold — you learn whether students can name the error, not just avoid it.
3. Run the problem backwards
DOK 2–3: A mix uses a 3 : 1 ratio. A student made 16 cups of lemonade total. How much of each ingredient did they use, and how do you know?
Working from the total back to the parts forces students to reason about the structure of the ratio instead of scaling a table forward.
4. Give more information than they need
Including one irrelevant quantity turns “apply the procedure” into “decide what matters.” Use this sparingly — one extra quantity, clearly stated. Three become a reading test.
The trap: rigor that’s really reading load
Long word problems, dense contexts, and unfamiliar vocabulary raise difficulty without raising DOK, and they penalize multilingual learners and struggling readers for something you weren’t trying to measure. If you can cut fifteen words without changing the thinking required, cut them.
A useful check: read the item aloud. If a student who understands the math would still be stuck after hearing it, the barrier is language, not depth.
Balance the set, don’t maximize it
An assessment that’s all DOK 3 tells you who can argue and nothing about who can compute. A workable shape for a formative check:
dok_1: 1 item — confirms the procedure is in place
dok_2: 3 items — the working core of the assessment
dok_3: 1 item — constructed response, scored with a rubric
note: keep reading load constant across items
The DOK 1 item isn’t filler — it’s your control. When a student misses the DOK 3 item but nails the DOK 1, you know it’s reasoning. When they miss both, you know it’s the procedure. That distinction is the entire point of giving the assessment.
Score DOK 3 with a rubric, or don’t ask for it
An open item without a rubric becomes a grading argument at 9pm. Three levels is enough for a formative check: full reasoning, correct-but-unjustified, and no valid comparison. Write it before you give the assessment, not after.