“When are we ever going to use this?” No joke, years in the past my division coverage to reply to college students was “We are teaching you critical thinking.” Is math instructing vital pondering? I can’t converse for all math lessons, however our curriculum was undoubtedly NOT. Once I realized about Depth of Knowledge (DOK) I spotted 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 academics we’re conscious of what vital pondering appears like in math.

The 4 Levels of DOK

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

• Level 1: Recall and Reproduction – Students are requested to recall data and reproduce beforehand realized ideas.
• Level 2: Skills and Concepts – Students are requested to use abilities and ideas they’ve realized to resolve issues or carry out duties.
• Level 3: Strategic Thinking – Students are requested to motive, plan, and use proof to resolve advanced issues or full advanced duties.
• Level 4: Extended Thinking – Students are requested to make connections between concepts, synthesize data, and switch data to new conditions.

“Live in DOK 2 and DOK 3. Visit DOK 1 and DOK 4”

-Shelley Burgess

Students ought to be critically pondering in math class. This implies that most of what we ask college students to do ought to be no less than DOK 2.

Mathematics DOK Definitions

It is hard to categorize math duties to the proper DOK ranges. We typically mistake laborious for being advanced. This article from WebbAlign comprises some useful recommendations on what the 4 ranges of DOK are.

The final aim of utilizing DOK ranges in math instruction is to offer a extra significant and difficult studying expertise for college kids.

Highlights From the Article

DOK 1

Following steps is DOK 1 as is “executing a well-defined multi-step procedure.” A math downside can require a number of steps and nonetheless be low vital pondering. “Operating on polynomials or radicals, using the laws of exponents, or simplifying rational expressions are considered rote procedures.”

It is admittedly necessary to grasp that DOK is just not in regards to the verbs. Try to keep away from the DOK wheel that’s prevalent in Google searches for Depth of Knowledge. It is the extent of advanced reasoning by the scholar that defines the DOK degree, not the phrases used within the job.

DOK 2

Students must do their very own pondering for it to be thought of DOK 2. My fast and soiled for DOK is “how much figure it out is there?” So it’s not the variety of steps it might require, however somewhat “engaging in some mental processing beyond a habitual response as well as decision-making…”

If I have been to present you a really giant binder with 1 million steps to place collectively a rocket to the moon, this job could be very tough. You would most likely make a mistake someplace. However, if you happen to 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 elevate this job to DOK 2 you would want to have some ambiguous components of the instructions, maybe extra like IKEA instructions, that may require you determine some steps.

Asking to scholar to clarify their reasoning is probably going a DOK 2 job. This is completely different from present your work. Listing out the steps in phrases remains to be recalling the steps and procedures. Students would want to clarify why they made a specific choice that goes past recalling the rule.

DOK 3

“DOK 3 requires reasoning and analyzing.” Mathematical reasoning is just not recalling math procedures and formulation. Mathematical reasoning is way. extra advanced. This is what hopefully college students acquire from taking math lessons is the flexibility to motive by means of a state of affairs and determine what math they should apply and the way to apply it. Mathematical reasoning doesn’t must contain numbers. It is the strategic pondering by means of of an issue and logically determining an answer.

“DOK 3 includes situations that are nonroutine, more demanding, more abstract, and more complex than DOK 2.”

Where DOK will get difficult is that it’s not simply the outline of the duty to take into accounts. “Note that the sophistication of a mathematical argument that would be considered DOK 3 depends on the prior knowledge and experiences of the person.” Prior data can change the DOK degree of a job for a scholar.

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

DOK 4

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 know-how of DOK. You could be doing fairly good to do DOK 4 a couple of times a faculty 12 months.

DOK 4 sometimes has “the need to perform activities over days and weeks (DOK 4) rather than in one sitting…” While it’s not essentially a challenge or analysis exercise, it might be extraordinarily tough for college kids to realize advanced reasoning in a single day. The figuring out issue is NOT time, nonetheless. “The extended time period is not a distinguishing factor if the required work is only repetitive and does not require applying significant conceptual understanding and higher-order thinking.”

Is Coding DOK 4?

Is coding DOK 4? Coding is a verb and it’s not the verb that determines the DOK degree. When I first realized to code JavaScript after which wished 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 data of JavaScript and prolonged it to determine the way it utilized in a special context of Google Apps Script.

I had an unique challenge concept and must adapt what I knew to a brand new state of affairs. This was DOK 4 reasoning. However, right this moment if I wished to code in Google Apps Script I’m most likely at greatest doing DOK 2 degree reasoning and probably 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, nonetheless, now this can be a DOK 1 job. I now not should determine it out.

Difficult Vs. Complex

One of the explanations 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.

Just as a result of it’s laborious doesn’t make it advanced.

Notice within the graphic under that on a matrix of advanced and tough that math duties are generally excessive problem however low complexity. Meaning they’re DOK 1, however college students battle with them.

Surely, if a scholar is doing Calculus they’re doing DOK 4. Actually, many of the Calculus guide I had in school was DOK 1. If the guide offers you the method and then you definately use it to do apply issues then it’s doing the pondering for the scholar and thus DOK 1.

Robert Kaplinsky

Robert Kaplinsky is, in my view, the skilled in math DOK. If you want to improve the DOK of your class take a while to learn Robert Kaplinsky’s weblog. He can also be the founding father of Open Middle. There are DOK 2 and DOK 3 degree math issues. Notice they don’t seem to be DOK 4 degree math issues as a result of, once more, DOK 4 is just not the aim!

Building Thinking Classrooms

The guide “Building Thinking Classrooms” by Peter Liljedahl took a analysis based mostly method to discovering the way to get college students to do extra pondering in a math classroom. The guide is a straightforward learn and transformational in how we method instructing math. Join the Facebook group.

Is Math Teaching Critical Thinking?

Analyze Current DOK Levels

Start by reviewing your present math issues to establish their present DOK degree. This will show you how to establish areas the place you’ll be able to improve the cognitive complexity of the duties. Firstly, assessment…

Develop Learning Objectives

Next, concentrate on growing studying targets that require higher-order pondering abilities, reminiscent of evaluation, synthesis, and analysis. Secondly, develop…

Increase Complexity

Design math issues that align with the training targets you may have developed. Ensure that these issues problem college students to use what they’ve realized in new and complicated methods. Moreover, design…

Incorporate Real-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. Furthermore, incorporate…

Design Rubrics

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

By following these steps, you’ll be able to improve the DOK ranges of the maths issues you create, offering a extra significant and difficult studying expertise on your college students. Is Math Teaching Critical Thinking? It may very well be!