April 13, 2024

“When are we ever going to make use of this?” No joke, years in the past my division coverage to answer college students was “We’re educating you vital pondering.” Is math educating vital pondering? I can’t communicate for all math courses, however our curriculum was positively NOT. As soon as I realized about Depth of Information (DOK) I noticed that almost all of the textbook and all of our worksheets have been low vital pondering, DOK 1. I believe the aim of math class ought to be to show vital pondering so it is necessary that as math lecturers we’re conscious of what vital pondering seems like in math.

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

The 4 Ranges of DOK

There are 4 ranges of DOK to explain the degrees of vital pondering.

  • Stage 1: Recall and Copy – College students are requested to recall data and reproduce beforehand realized ideas.
  • Stage 2: Expertise and Ideas – College students are requested to use expertise and ideas they’ve realized to unravel issues or carry out duties.
  • Stage 3: Strategic Considering – College students are requested to purpose, plan, and use proof to unravel advanced issues or full advanced duties.
  • Stage 4: Prolonged Considering – College students are requested to make connections between concepts, synthesize data, and switch information to new conditions.

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

-Shelley Burgess

College students ought to be critically pondering in math class. Which means most of what we ask college students to do ought to be not less than DOK 2.

Arithmetic DOK Definitions

It’s tough to categorize math duties to the proper DOK ranges. We regularly mistake exhausting for being advanced. This text from WebbAlign accommodates some useful tips about what the 4 ranges of DOK are.

The last word aim of utilizing DOK ranges in math instruction is to offer 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 downside can require a number of steps and nonetheless be low vital pondering. “Working on polynomials or radicals, utilizing the legal guidelines of exponents, or simplifying rational expressions are thought of rote procedures.”

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

It’s actually vital to know that DOK just isn’t in regards to the verbs. Attempt to keep away from the DOK wheel that’s prevalent in Google searches for Depth of Information. It’s the stage of advanced reasoning by the scholar that defines the DOK stage, not the phrases used within the job.

Present your work is DOK 1.


College students have to do their very own pondering for it to be thought of DOK 2. My fast and soiled for DOK is “how a lot determine it out is there?” So it isn’t the variety of steps it could require, however fairly “participating in some psychological processing past a ordinary response in addition to decision-making…”

If I have been to offer you a really giant binder with 1 million steps to place collectively a rocket to the moon, this job could be very troublesome. You’d in all probability make a mistake someplace. Nonetheless, if you happen to adopted all 1 million steps completely the rocket would go to the moon. Rocket constructing is a DOK 1 job if you’re 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 might require you determine some steps.

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


“DOK 3 requires reasoning and analyzing.” Mathematical reasoning just isn’t recalling math procedures and formulation. Mathematical reasoning is way. extra advanced. That is what hopefully college students achieve from taking math courses is the flexibility to purpose by way of a state of affairs and determine what math they should apply and easy methods to apply it. Mathematical reasoning doesn’t have to contain numbers. It’s the strategic pondering by way of of an issue and logically determining an answer.

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

The place DOK will get tough is that it isn’t simply the outline of the duty to consider. “Word that the sophistication of a mathematical argument that might be thought of DOK 3 relies on the prior information and experiences of the individual.” Prior information can change the DOK stage of a job for a scholar.

In case you anticipate a scholar to get it proper the primary time, it isn’t DOK 3.


I can not emphasize sufficient that the aim is NOT DOK 4. Requiring day by day DOK 4 duties in math merely demonstrates a lack of knowledge of DOK. You’d be doing fairly good to do DOK 4 a few times a college 12 months.

DOK 4 sometimes has “the necessity to carry out actions over days and weeks (DOK 4) fairly than in a single sitting…” Whereas it isn’t essentially a challenge or analysis exercise, it could be extraordinarily troublesome for college students to attain advanced reasoning in a single day. The figuring out issue is NOT time, nonetheless. “The prolonged time interval just isn’t a distinguishing issue if the required work is simply repetitive and doesn’t require making use of important conceptual understanding and higher-order pondering.”

Is Coding DOK 4?

Is coding DOK 4? Coding is a verb and it isn’t the verb that determines the DOK stage. After I first realized to code JavaScript after which needed to put in writing 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 information of JavaScript and prolonged it to determine the way it utilized in a unique context of Google Apps Script.

I had an authentic challenge concept and have to adapt what I knew to a brand new state of affairs. This was DOK 4 reasoning. Nonetheless, right this moment if I needed to code in Google Apps Script I’m in all probability at greatest doing DOK 2 stage reasoning and presumably DOK 1. If I can effortlessly produce a script with out making an error I’m utilizing my recall expertise. The identical job of making code to rearrange scholar names into tabs of a spreadsheet was DOK 4 for me, nonetheless, now this can be a DOK 1 job. I not need to determine it out.

Troublesome Vs. Advanced

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 advanced reasoning.

Simply because it’s exhausting doesn’t make it advanced.

Discover within the graphic under that on a matrix of advanced and troublesome 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. Truly, many of the Calculus e-book I had in faculty was DOK 1. If the e-book provides you the method and then you definately use it to do follow issues then it’s doing the pondering for the scholar and thus DOK 1.

Robert Kaplinsky

Robert Kaplinsky is, for my part, the professional in math DOK. In case you are seeking to enhance 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 stage math issues. Discover they aren’t DOK 4 stage math issues as a result of, once more, DOK 4 just isn’t the aim!

Constructing Considering School rooms

The e-book “Constructing Considering School rooms” by Peter Liljedahl took a analysis based mostly method to discovering easy methods to get college students to do extra pondering in a math classroom. The e-book is a simple learn and transformational in how we method educating math. Join the Facebook group.

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Is Math Instructing Vital Considering?

Analyze Present DOK Ranges

Begin by reviewing your present math issues to establish their present DOK stage. This can provide help to establish areas the place you possibly can enhance the cognitive complexity of the duties. Firstly, evaluation…

Develop Studying Targets

Subsequent, deal with growing studying goals that require higher-order pondering expertise, corresponding to evaluation, synthesis, and analysis. Secondly, develop…

Enhance Complexity

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

Incorporate Actual-World

Incorporate real-world eventualities or knowledge 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 provide help to assess scholar efficiency and supply suggestions that may information their studying. Lastly, create…

By following these steps, you possibly can enhance the DOK ranges of the mathematics issues you create, offering a extra significant and difficult studying expertise on your college students. Is Math Instructing Vital Considering? It might be!