Depth of Knowledge in Math K-5 Math Back to School Conference August 1, 2014 Gardendale High School

K-5 Math Survey Depth of Knowledge Small Group Instruction Number Talks

Session Outcomes Participants will learn the importance of DOK in mathematics. Participants will identify the DOK levels of K-5 Math Tasks.

What is DOK?

Depth of Knowledge (D.O.K.) Measures the degree to which the knowledge elicited from students on assessments is as complex as what students are expected to know and do as listed in the state standards.

What Do Depth of Knowledge Assessments Accomplish? DOK assessments are a mechanism to ensure that the intent of the standard and the level of student demonstration required by that standard match.

D.O.K. Compared to Bloom’s Bloom’s taxonomy level of difficulty is determined by the verb. DOK’s level of cognitive demand is determined by the context of how the verb is used and the depth of thinking required. What comes after the verb is more important that the verb itself.

Depth of Knowledge Level 1 Conduct basic mathematical calculations Label locations Perform routine procedures RECALL Determine the perimeter or area of rectangles given a drawing or labels

Depth of Knowledge Level Two Solve routine multiple-step problems Identify patterns Organize, represent and interpret data SKILLS AND/OR CONCEPT Classify plane and three dimensional figures

Depth of Knowledge Level Three Apply a concept in other contents Support ideas with details and examples STRATEGIC THINKING Solve a multiple-step problem and provide support with a mathematical explanation that justifies the answer

Depth of Knowledge Level Four Apply mathematical model to illuminate a problem or situation. Analyze and synthesize information from multiple sources Design a mathematical model to inform and solve a practical or abstract situation EXTENDED THINKING

Applying DOK Levels in Math What do you notice?

Depth of Knowledge (DOK) Activity : Depth of Knowledge Math Sorting Activity Working individually, classify each mathematical assessment task according to its DOK level. Work with a partner to arrive at consensus as to what DOK level each task reflects. Report out responses and the rationale of such responses. Provide participants with envelope containing the Depth of Knowledge Math Sorting Activity already cut for them. In addition, provide participants with Depth of Knowledge Cognitive Levels chart. The participants will categorize each of the tasks in their envelope under one of the DOK levels on their chart. All tasks in column 1 should represent DOK level 1; all tasks in column 2 represent DOK level 2, etc. In this activity, we will take each learning activity from the envelope and place it under the appropriate column on the Depth of Knowledge Cognitive Levels chart. For example, the activity of measuring areas by counting unit squares (square cm, square m, square in, square ft), and improvised units corresponds to the DOK level 1. The activity of finding and positioning integers and other rational numbers on a horizontal or vertical number line diagram; finding and positioning pairs of integers and other rational numbers on a coordinate plane represents the DOK 2. Begin by working individually to classify each mathematical task according to its DOK level. Then work with a partner to come to a consensus as to which DOK level each mathematical task represents. Provide 5 minutes for individual work. Participants should then work with a partner to come to a consensus as to which DOK level each mathematical task represents. Provide 6 minutes for partner work. Participants may report to the group their responses and the rationale. The emphasis of the discussion as participants report should stem from WHY participants selected specific DOK levels.   Copyright ©2010 Commonwealth of Pennsylvania

How did you do?

DOK 1- 1MD.2

DOK 2 – 1.NBT.2

DOK 1- 2.NBT.4

DOK 2- 2.OA.3

DOK 3- 2.NBT.8

DOK 1 – 4.NF.2

DOK 2- 3.OA.6

DOK 1- 3.OA.6

DOK 2- 5.NBT.7

DOK 2- 3.OA.3

Depth of Knowledge So what is the point of knowing Depth of Knowledge? This helps us understand what the outcomes of our lessons should be. We need to prepare students to think more conceptually

Questions to Consider When Assessing Learning… What DOK levels should you be targeting with assessment questions? What would you consider to be an appropriate distribution of the different DOK levels in an assessment? What concerns do you have regarding the different levels of DOK? How might you build DOK Level 4 questions into your unit/lesson/assessment design?

Remember… Depth of Knowledge (DOK) is a scale of cognitive demand. DOK requires looking at the assessment item/standard – not student work – in order to determine the level. DOK is about the item/standard – not the student. The context of the assessment item/standard must be considered to determine the DOK – not just a look at what verb was chosen. An item/standard written to DOK 3 often contains DOK 1 and DOK 2 level demands.

3, 2, 1, Exit Ticket 3 Things you will do to utilize this information about DOK in Math 2 Things you discovered about DOK in Math 1 Question you still have