Depth of Knowledge in Math


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This presentation has/will be used with K-12 Math teachers to explore the concept of Depth of Knowledge in order to apply this information to resources and assessments in order to insure there is an appropriate level of DOK in our courses.

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  • Video from NYC Schools
  • The work we have is from AERO but this is based on the PARCC documents, the group that is developing curriculum and assessment guidelines. Let’s also all remember this is all very new and resources are coming out fast and furious.
  • Level One – Recall: fact, information, procedureLevel Two – Skill/Concept: Two or more steps and use of informationLevel Three – Strategic Thinking: requires reasoning, developing a plan or a sequence of steps, some complexity, more than one answerLevel Four – Extended Thinking: requires investigation, time to think and process multiple conditions of the problem.
  • a (1): harsh inflexibility in opinion, temper, or judgment :severity(2): the quality of being unyielding or inflexible :strictness(3): severity of life :austerityb: an act or instance of strictness, severity, or cruelty 2: a tremor caused by a chill 3: a condition that makes life difficult, challenging, or uncomfortable; especially: extremity of cold 4: strict precision :exactness <logical rigor>
  • Complex, multistep tasks that require decisions, evaluation, justification, have greater rigor.
  • This time it is about having the resources to help you get the students to the higher level tasks.
  • We will go over each one of these more indepth.
  • Nothing more than recalling or reciting is generally used. It is a DOK 1, not 2But in Blooms, explain is often an indication of a higher order taskJump off to a discussion of the importance of looking at task.2 requires congitive processing to determine the difference in the two rock types
  • Ask teachers to distinguish the levels and why2 requires cognitive processing to determine the difference in the two rock types1 requires simple recall3 requires deep understanding of rock cycles and a determination of how best to represent it.
  • It is DOK 1, it is difficult, but it is about the rule, the algorythem. Once you know the rule, you know how to add 4 + 1, you just apply this same rule to the above. It is more difficult, but it is still DOK1
  • What they mean by distinguishing factor is…for example if a student has to take the water temperature from a river each day for a month and then construct a graph, this is DOK 2,However, if they conduct a river study that requires them to take into account a number of variables, this would be a level 4
  • Depth of Knowledge in Math

    1. 1. Stacy Stephens<br />Introduction to Depth of Knowledge (DoK)<br />
    2. 2. Overview of Depth of Knowledge<br />
    3. 3. <ul><li>A scale of cognitive demand (thinking)
    4. 4. Based on research of Norman Webb, University of Wisconsin Center for Education and the National Institute for Science Education
    5. 5. DOK levels have been assigned to the Common Core Standards
    6. 6. State and national assessments will test at this level</li></ul>What it is<br />
    7. 7. Depth of Knowledge Levels<br />1<br />2<br />3<br />Extended Thinking - requires investigation, time to think and process multiple conditions of the problem.<br />4<br />
    8. 8. The kind and level of thinking required of students to successfully engage and solve a task.<br />The ways in which students interact with content<br />It is about complexity, not difficulty<br />It is about rigor<br />
    9. 9. Focus on complexity of content standards in order to successfully complete an assessment or task. The outcome (product) is the focus of the depth of understanding<br />Rigor is about Complexity<br />
    10. 10. To clarify the intent of the standard and level of student demonstration required by the indicator matches the resources and assessment tasks.<br />Again…it is about rigor.<br />Why Designate DOK in the CCSS?<br />
    11. 11. <ul><li>It is not equivalent to Bloom’s
    12. 12. Is not the same as difficulty
    13. 13. Is not about the “verb”</li></ul>Depth of Knowledge is not:<br />
    14. 14. The DOK is not about the verb associated with it (like Bloom’s), rather the DOK is about the context in which the verb is used and the depth of thinking required.<br />What comes after the verb is more important than the verb itself<br />It is not about the verb<br />
    15. 15. You cannot use verbs alone to determine DOK<br />Words like explain or analyze have to be considered in context<br />What is the DOK Level or complexity of?<br />Explain to me where you live.<br />Example<br />
    16. 16. <ul><li>Describe the difference between metamorphic and igneous rocks
    17. 17. Describe three characteristics of metamorphic rocks.
    18. 18. Describe a model that you might use to represent the relationships that exist within the rock cycle</li></ul>Same verb – 3 different dok levels<br />
    19. 19. Add:<br />4,678,895 + 9,578,885<br />What is the DOK?<br />DOK is not the Same as difficulty<br />
    20. 20. <ul><li>The DOK level tells us how deep to go with a standard
    21. 21. In Math DOK levels have been assigned to the indicators
    22. 22. Instruction, resources used, and assessments need to be targeted at that DOK level</li></ul>DOK is about Complexity<br />
    23. 23. DOK in Math<br />
    24. 24. Fact, definition, term, or a simple procedure<br />Performing simple algorithms or applying a formula<br />Key words: identify, recall, recognize, use, and measure<br />Caution, verbs like explain and describe could be classified at a different level depending on the task<br />Level One: Recall<br />
    25. 25. Engagement in some mental process beyond a habitual response<br />Requires some decision as to how to approach the problem<br />Keywords: classify, organize, estimate, make observations, collect and display data, and compare data. Implied there is more than one step<br />Example: if an item required students to explain how light affects mass by indicating there is a relationship between light and heat, this is level two<br />Activities: carry out an experiment, explain the purpose of procedures, make observations and collect data, classify, organize, and compare data, etc.<br />Level Two: Skill/Concept<br />
    26. 26. Requires reasoning, planning, using evidence<br />In most instances, requiring student to explain their thinking or requiring conjectures are level 3<br />These are more demanding than previous levels. Demands are complex and abstract, not just many answers (sometimes this can happen at 1 and 2)<br />An activity with more than one possible answer, but requiring selection and justification is most likely this level<br />Other level 3 activities: drawing conclusions from observations, citing evidence and developing logical arguments, explaining phenomena in terms of concepts, using concepts to solve problems<br />Level three: Strategic Thinking<br />
    27. 27. Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time (though this is not a distinguishing factor)<br />Students are required to make several connections and relate ideas within or among the content areas<br />Students are required to select one approach among many alternatives about how the situation should be solved<br />Activities include: designing and conducting experiments, making connections between a finding and related concepts and phenomena, combining and synthesizing ideas into new concepts, and critiquing experimental designs<br />Level Four: Extended thinking<br />
    28. 28. Using your resource, select an assessment or lesson<br />Then cross-reference your Clarification Documents from AERO where the DOK levels are laid out with the indicators<br />Use the DOK rubric to do an item analysis vis a vis the standard and the designated DOK level<br />QUESTION: DOES IT MEET THE REQUIRED LEVEL OF RIGOR?<br />Application<br />
    29. 29. Teaching with Depth, ppt. presentation from Florida State School District<br />Cindy Simmons, Office of Assessment, Mississipppi State Department of Education Aug. 2007<br />Norman Webb, University of Wisconsin, March 2002<br />Images:<br />Jimmyhomescoolmom from Flickr<br />Bloom’s from<br />Citations<br />