## September 2014

### An Assistant Superintendent from Missouri asks...

“In reading lots of research and information over the years about DOK, and now your cognitive rigor matrix, I find that there's tension between the ideas that DOK involves complexity of thought on the part of the learner and that DOK is grounded in the standard itself rather than the context.

Specifically, I'm questioning standards (particularly in math) that are taught and learned as concepts (DOK 2) to young children but later expected to be rote knowledge by older students. If a kindergartener is solving 9+5 that would seem to involve a far different 'complexity of thought' than a 3rd grader answering the same question?”

Dr. Hess answers...

I get questions like this all of time and I am happy to share my view… I always try to interpret Norman Webb’s work honestly and see lots of conflicting information out there.

First of all, the age of a learner does not determine DOK levels. Anything that is “routine” can be memorized is generally categorized a DOK 1 task – learning to add, doing long division, or evaluating an expression. Even though these might involve multiple steps, once you learn how to do them, they are routine and you can practice them in the same way with many different problems.

Reading examples, such as finding the main idea or summarizing key ideas, are DOK 2, not because there are multiple steps, but multiple decisions to be made requiring an understanding of more than one concept or seeing relationships among concepts/ideas. DOK 2 includes math word problems, making observations, making predictions, etc.

What pushes a task to DOK 3 or DOK 4 (which means multiple sources/texts are needed to solve it) is that it may have more than one approach or correct answer (e.g., determining theme) and requires justification and/or explanations of reasoning. Telling the steps I used to solve a problem is DOK 2; proving why this answer is reasonable is DOK 3.

Most math CC content standards are written at a DOK 1 or 2 – skills and procedures are DOK 1 and conceptual understanding is DOK 2. A teacher should always put more emphasis on DOK 2/conceptual before introducing procedural routines…so effective teaching is based in DOK 2 (conceptual understanding). What pushes math content standards to DOK 3+ are SOME of the math practices: developing a math argument, critiquing the work of others, solving non-routine problems. For example, see the handout I give at workshops, “Find a Half” – with many routine and non-routine representations of a half or not half. Explanations require reasoning (DOK 3) based on conceptual understanding (DOK 2) and skills (DOK 1, counting). See also my quick analysis of find a half.

It is not until you combine content standards with particular math practices, that you reach DOK 3 or 4 in math.

Now back to one last critical point about how math is taught and what becomes “rote” later on…I often hear K-2 teachers especially say/question what is DOK 2 or DOK 1, depending on how it is taught or learned…bottom line is that if there is a correct answer, it is DOK 1 OR DOK 2.

There is a difference between hard to do (difficulty at first) and complex (deep and open-ended tasks).

DOK is not about difficulty of the task. Many things that become rote with practice through multiple /varied exposures were hard to do at first – learning to drive or to ski, for example, required many skills becoming rote. Lots of practice/drills was needed to learn to drive (DOK 1) integrated with connecting what the law says (DOK 1) with under what circumstances (DOK 2 – when you see a stop sign, you apply brakes and stop/cause-effect). The most effective teachers actually base their teaching in DOK 3 discourse (let’s talk about why that worked, what skills did you use, what was your reasoning, etc.) and challenging tasks requiring an understanding of concepts and how to apply skills. There is research to support that DOK 3-based teaching is more engaging for all levels of students (cited in my new paper with B. Gong, Ready for College & Career? posted on the Nellie Mae website)

So, using manipulatives to demonstrate how sets can be joined is an engaging & conceptual way to introduce the concept of addition (a generalization). Giving a more complex task where students must show whyjoining sets is the right approach and breaking a set apart is not the right approach for a given situation to answer a question is more complex that simply counting (DOK 1) or using manipulatives (DOK 2). I suggest that teachers ask, why am I teaching it this way? Do I expect this to become rote? Can it become rote/memorized with practice?

When (age/grade) and how you learn something does not determine DOK level.

Summarizing a complex text is DOK 2; summarizing a simple text is also DOK 2. The text (or context) may influence the difficulty of completing the task, just as magnitude of numbers will – easy to add single digit numbers and harder to add 3-digit numbers…it is still routine. It is still adding.

- Dr. DoK