April 16, 2024

“When are we ever going to make use of this?” No joke, years in the past my division coverage to reply to college students was “We’re instructing you important considering.” Is math instructing important considering? I can’t communicate for all math courses, however our curriculum was positively NOT. As soon as I realized about Depth of Data (DOK) I spotted that almost all of the textbook and all of our worksheets had been low important considering, DOK 1. I believe the aim of math class must be to show important considering so it will be important that as math lecturers we’re conscious of what important considering seems to be like in math.

Depth of Data (DOK) is a framework that categorizes duties primarily based on their cognitive complexity and the extent of considering required to finish them.

The 4 Ranges of DOK

There are 4 ranges of DOK to explain the degrees of important considering.

  • Degree 1: Recall and Copy – College students are requested to recall info and reproduce beforehand realized ideas.
  • Degree 2: Abilities and Ideas – College students are requested to use abilities and ideas they’ve realized to resolve issues or carry out duties.
  • Degree 3: Strategic Pondering – College students are requested to motive, plan, and use proof to resolve complicated issues or full complicated duties.
  • Degree 4: Prolonged Pondering – College students are requested to make connections between concepts, synthesize info, and switch data to new conditions.

“Stay in DOK 2 and DOK 3. Go to DOK 1 and DOK 4”

-Shelley Burgess

College students must be critically considering in math class. Because of this most of what we ask college students to do must be at the least DOK 2.

Arithmetic DOK Definitions

It’s difficult to categorize math duties to the proper DOK ranges. We regularly mistake laborious for being complicated. This text from WebbAlign incorporates some useful recommendations on what the 4 ranges of DOK are.

The last word purpose of utilizing DOK ranges in math instruction is to supply a extra significant and difficult studying expertise for college students.

Highlights From the Article


Following steps is DOK 1 as is “executing a well-defined multi-step process.” A math drawback can require a number of steps and nonetheless be low important considering. “Working on polynomials or radicals, utilizing the legal guidelines of exponents, or simplifying rational expressions are thought-about rote procedures.”

“Verbs shouldn’t be categorised as any class…”

It’s actually necessary to grasp that DOK will not be concerning the verbs. Attempt to keep away from the DOK wheel that’s prevalent in Google searches for Depth of Data. It’s the degree of complicated reasoning by the scholar that defines the DOK degree, not the phrases used within the job.

Present your work is DOK 1.


College students must do their very own considering for it to be thought-about DOK 2. My fast and soiled for DOK is “how a lot determine it out is there?” So it’s not the variety of steps it might require, however relatively “participating in some psychological processing past a routine response in addition to decision-making…”

If I had been to offer you a really massive binder with 1 million steps to place collectively a rocket to the moon, this job could be very tough. You’d in all probability make a mistake someplace. Nevertheless, when you adopted all 1 million steps completely the rocket would go to the moon. Rocket constructing is a DOK 1 job in case you are solely following the instructions. To raise this job to DOK 2 you would want to have some ambiguous components of the instructions, maybe extra like IKEA instructions, that will require you determine some steps.

Asking to scholar to clarify their reasoning is probably going a DOK 2 job. That is totally different from present your work. Itemizing out the steps in phrases continues to be recalling the steps and procedures. College students would want to clarify why they made a selected choice that goes past recalling the rule.


“DOK 3 requires reasoning and analyzing.” Mathematical reasoning will not be recalling math procedures and formulation. Mathematical reasoning is way. extra complicated. That is what hopefully college students achieve from taking math courses is the power to motive via a state of affairs and determine what math they should apply and how you can apply it. Mathematical reasoning doesn’t must contain numbers. It’s the strategic considering via of an issue and logically determining an answer.

“DOK 3 consists of conditions which are nonroutine, extra demanding, extra summary, and extra complicated than DOK 2.”

The place DOK will get difficult is that it’s not simply the outline of the duty to take into accounts. “Observe that the sophistication of a mathematical argument that will be thought-about DOK 3 is dependent upon the prior data and experiences of the individual.” Prior data can change the DOK degree of a job for a scholar.

Should you count on a scholar to get it proper the primary time, it’s not DOK 3.


I can’t emphasize sufficient that the purpose is NOT DOK 4. Requiring each day DOK 4 duties in math merely demonstrates a lack of information of DOK. You’d be doing fairly good to do DOK 4 a few times a faculty 12 months.

DOK 4 sometimes has “the necessity to carry out actions over days and weeks (DOK 4) relatively than in a single sitting…” Whereas it’s not essentially a venture or analysis exercise, it might be extraordinarily tough for college students to realize complicated reasoning in a single day. The figuring out issue is NOT time, nevertheless. “The prolonged time interval will not be a distinguishing issue if the required work is barely repetitive and doesn’t require making use of important conceptual understanding and higher-order considering.”

Is Coding DOK 4?

Is coding DOK 4? Coding is a verb and it’s not the verb that determines the DOK degree. After I first realized to code JavaScript after which wished to jot down my first Add-on for Google Sheets in Google Apps Script I needed to do a LOT of determine it out. I used to be not following a tutorial with steps and instructions.Taking my data of JavaScript and prolonged it to determine the way it utilized in a special context of Google Apps Script.

I had an authentic venture concept and must adapt what I knew to a brand new state of affairs. This was DOK 4 reasoning. Nevertheless, as we speak if I wished to code in Google Apps Script I’m in all probability at finest doing DOK 2 degree reasoning and presumably DOK 1. If I can effortlessly produce a script with out making an error I’m utilizing my recall abilities. The identical job of making code to rearrange scholar names into tabs of a spreadsheet was DOK 4 for me, nevertheless, now it is a DOK 1 job. I now not need to determine it out.

Tough Vs. Complicated

One of many causes it may be so difficult to align a math job to DOK is the notion that if a scholar struggles with it they should be doing complicated reasoning.

Simply because it’s laborious doesn’t make it complicated.

Discover within the graphic beneath that on a matrix of complicated and tough that math duties are generally excessive problem however low complexity. Which means they’re DOK 1, however college students wrestle with them.

Is Math Teaching Critical Thinking? most common are problems that are hard but not complex. this shows a qudarant of difficulty low to high and complexity low to high. Most common are the upper left low complexity and high difficulty.

Absolutely, if a scholar is doing Calculus they’re doing DOK 4. Really, a lot of the Calculus guide I had in faculty was DOK 1. If the guide provides you the formulation and then you definitely use it to do follow issues then it’s doing the considering for the scholar and thus DOK 1.

Robert Kaplinsky

Robert Kaplinsky is, in my view, the knowledgeable in math DOK. If you’re seeking to improve the DOK of your class take a while to learn Robert Kaplinsky’s weblog. He’s additionally the founding father of Open Center. There are DOK 2 and DOK 3 degree math issues. Discover they aren’t DOK 4 degree math issues as a result of, once more, DOK 4 will not be the purpose!

Constructing Pondering School rooms

The guide “Constructing Pondering School rooms” by Peter Liljedahl took a analysis primarily based strategy to discovering how you can get college students to do extra considering in a math classroom. The guide is a simple learn and transformational in how we strategy instructing math. Join the Facebook group.

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Is Math Educating Vital Pondering?

Analyze Present DOK Ranges

Begin by reviewing your current math issues to establish their present DOK degree. This may make it easier to establish areas the place you may improve the cognitive complexity of the duties. Firstly, assessment…

Develop Studying Targets

Subsequent, concentrate on creating studying goals that require higher-order considering abilities, comparable to evaluation, synthesis, and analysis. Secondly, develop…

Enhance Complexity

Design math issues that align with the educational goals you could have developed. Be sure that these issues problem college students to use what they’ve realized in new and sophisticated methods. Furthermore, design…

Incorporate Actual-World

Incorporate real-world situations or information units into the issues to extend the authenticity and relevance of the duties. By doing so, college students will be capable of see the sensible utility of what they’re studying. Moreover, incorporate…

Design Rubrics

Create rubrics that align with the DOK ranges of the issues you could have designed. These rubrics will make it easier to assess scholar efficiency and supply suggestions that may information their studying. Lastly, create…

By following these steps, you may improve the DOK ranges of the maths issues you create, offering a extra significant and difficult studying expertise to your college students. Is Math Educating Vital Pondering? It might be!