Explanation of Webb’s DOK Related to Mathematics

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Explanation of Webbs DOK Related to Mathematics

• Shelby County Schools
• Compiled by
• Allison Clark, Ed.D.
• Mathematics Curriculum Specialist, K-12
• aclark_at_scsk12.org
• Additional resources cited on last page

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Webbs Depth of Knowledge

• Model developed by Norman Webb, University of
  Wisconsin, Center for Education Research, to
  analyze alignment of standards with assessments.

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Definition

• Webb's Depth of Knowledge measures the levels
  of knowledge that are extracted from students on
  assessments is as complex as what students are
  expected to know and do as stated in the
  curriculum GLEs, SPIs, and Checks for
  Understanding.
• http//red6747.pbworks.com/Webb27s-Depth-Of-Knowl
  edge

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Related to TN Standards

• The 2009-2010 Tennessee Mathematics Standards
  reference DOK with the expectation that teachers
  will teach to a greater DOK.

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Webbs Depth of Knowledge
Levels

• Level 1 Recall and Reproduction
• Level 2 Skills Concepts
• Level 3 Strategic Thinking
• Level 4 Extended Thinking

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Level 1 Recall Reproduction

• Requires simple recall of such information as
  a fact, definition, term, or performance of a
  simple process or procedure. A student answering
  a Level 1 item either knows the answer or does
  not.

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Level 1 Examples

• List numbers from 0-5.
• Locate or recall facts about squares.
• Describe the attributes of a cube.
• Determine the perimeter or area of rectangles
  given a drawing or labels
• Identify basic rules for participating in simple
  games and activities

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Level 2 Skills Concepts

• Involves some mental skills, concepts, or
  processing beyond habitual response. Students
  must make some decisions about how to approach a
  problem or activity. Keywords distinguishing a
  Level 2 item include classify, organize, observe,
  estimate, collect data, and compare data.

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Level 2 Examples

• Compare fractions and decimals
• Identify and summarize the steps for solving a
  problem
• Explain the cause-effect of a given set of data
• Predict/estimate a logical outcome based on
  information in a chart or graph
• Explain how good work habits are important at
  home, school, and on the job
• Classify plane and three dimensional figures
• Describe qualitative change (the older you get,
  the taller you get)

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Level 3 Strategic Thinking

• Requires reasoning, planning, using evidence, and
  thinking at a higher level than the previous two
  levels. The complexity results because the
  multi-step task requires more demanding
  reasoning.
• An assessment item that has more than one
  possible answer and requires students to justify
  the response they give would most likely be a
  Level 3.

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Level 3 Examples

• Compose and decompose geometric figures to find
  area/perimeter of irregular figures
• Analyze or evaluate various representations of
  data
• Solve a multiple-step problem and provide support
  with a mathematical explanation that justifies
  the answer
• Explain, generalize or connect mathematical ideas
  to solve problems and interpret solutions

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Level 4 Extended Thinking

• Requires complex reasoning, planning,
  developing, and thinking, most likely over an
  extended time. Cognitive demands are high, and
  students are required to make connections both
  within and among subject domains.

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Level 4 Examples

• Relate mathematical concepts to other content
  areas
• Relate mathematical concepts to real-world
  applications in new situations
• Apply a mathematical model to illuminate a
  problem, situation
• Conduct a project that specifies a problem,
  identifies solution paths, solves the problem,
  and reports results
• Design a mathematical model to inform and solve a
  practical or abstract situation

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Same verbthree DOK levels

• SPI 3102.1.3 Apply properties to evaluate
  expressions, simplify expressions, and
• justify solutions to
  problems.
• Checks 3102.1.9 Identify and use properties of
  the real numbers (including
• commutative,
  associative, distributive, inverse, identity
  element,
• closure, reflexive,
  symmetric, transitive, operation properties of
• equality).
• Checks 3102.1.10 Use algebraic properties to
  develop a valid mathematical
• argument.
• Checks 3102.2.2  Apply the order of operations
  to simplify and evaluate algebraic
• expressions.
• Level 1- Identify the reflexive property. (simple
  recall)
• Level 2- Identify the math properties and
  summarize steps used to solve a multi-step
  problem. (requires cognitive processing to
  determine the differences in the math properties)
• Level 3- Identify the math properties used to
  solve a multi-step problem and provide support
  with a mathematical explanation that justifies
  the answer. (requires deep understanding of the
  math properties and a determination of how best
  to represent it)

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Additional Resources

• Wisconsin Center for Education Research
  http//wceruw.org
• Webbs Depth of Knowledge Levels for the K-12
  Tennessee Mathematics Framework Users Guide
• Kentucky Department of Education
• Tennessee 2009 Summer State Standards Training