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Explanation of Webb’s DOK Related to Mathematics

Explanation of Webb’s DOK Related to Mathematics. Shelby County Schools Compiled by: Allison Clark, Ed.D. Mathematics Curriculum Specialist, K-12 aclark@scsk12.org Additional resources cited on last page. Webb’s Depth of Knowledge.

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Explanation of Webb’s DOK Related to Mathematics

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  1. Explanation of Webb’s DOK Related to Mathematics Shelby County Schools Compiled by: Allison Clark, Ed.D. Mathematics Curriculum Specialist, K-12 aclark@scsk12.org Additional resources cited on last page

  2. Webb’s Depth of Knowledge Model developed by Norman Webb, University of Wisconsin, Center for Education Research, to analyze alignment of standards with assessments.

  3. Definition Webb's Depth of Knowledgemeasures 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/Webb%27s-Depth-Of-Knowledge

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

  5. Webb’s Depth of Knowledge Levels • Level 1 Recall and Reproduction • Level 2 Skills & Concepts • Level 3 Strategic Thinking • Level 4 Extended Thinking

  6. 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.

  7. 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

  8. 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.

  9. 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)

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. Same verb—three 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)

  15. Additional Resources • Wisconsin Center for Education Research http://wceruw.org • Webb’s Depth of Knowledge Levels for the K-12 Tennessee Mathematics Framework Users Guide • Kentucky Department of Education • Tennessee 2009 Summer State Standards Training

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