Differentiated Instruction and Critical Thinking

Frank Williams’ Taxonomy of Creative Thinking

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Frank Williams’ Taxonomy of Creative Thinking

  • Originality – We create clever and often unique responses to a prompt
  • Example Task: Define life and non-life.
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  • Elaboration – We expand upon or stretch an idea or thing, building on previous thinking
  • Example: What inferences about future algae growth can you make, given the three graphs of data from our experiment?

Frank Williams’ Taxonomy of Creative Thinking

  • Risk Taking – We take chances in our thinking, attempting tasks for which the outcome is unknown
  • Example: Write a position statement on whether or not genetic engineering of humans should be funded by the United States government.
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  • Complexity – We create order from chaos, we explore the logic of a situation, we integrate additional variables or aspects of a situation, contemplate connections
  • Example: Analyze how two different students changed their lab methodology to prevent data contamination.

Frank Williams’ Taxonomy of Creative Thinking

  • Curiosity – We pursue guesses, we wonder about varied elements, we question.
  • Example: What would you like to ask someone who has lived aboard the International Space Station for three months about living in zero-gravity?
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  • Imagination – We visualize ideas and objects, we go beyond just what we have in front of us
  • Example: Imagine building an undersea colony for 500 citizens, most of whom are scientists, a kilometer below the ocean’s surface. What factors would you have to consider when building and maintaining the colony and the happiness of its citizens?


  • R = Role, A = Audience, F = Form, T = Time or Topic, S = Strong adverb or adjective
  • Students take on a role, work for a specific audience, use a particular form to express the content, and do it within a time reference, such as pre-Civil War, 2025, or ancient Greece.
  • Sample assignment chosen by a student:
  • A candidate for the Green Party (role), trying to convince election board members (audience) to let him be in a national debate with Democrats and the Republicans. The student writes a speech (form) to give to the Board during the Presidential election in 2004 (time). Within this assignment, students use arguments and information from this past election with third party concerns, as well as their knowledge of the election and debate process. Another student could be given a RAFT assignment in the same manner, but this time the student is a member of the election board who has just listened to the first student’s speech.


  • Raise the complexity: Choose items for each category that are farther away from a natural fit for the topic . Example: When writing about Civil War Reconstruction, choices include a rap artist, a scientist from the future, and Captain Nemo.
  • Lower the complexity: Choose items for each category that are closer to a natural fit for the topic. Example: When writing about Civil War Reconstruction, choices include a member of the Freedmen’s Bureau, a southern colonel returning home to his burned plantation, and a northern business owner

Learning Menus

  • Similar to learning contracts, students are given choices of tasks to complete in a unit or for an assessment. “Entrée” tasks are required, they can select two from the list of “side dish” tasks, and they can choose to do one of the “desert” tasks for enrichment. (Tomlinson, Fulfilling the Promise of the Differentiated Classroom, 2003)

Tic-Tac-Toe Board

  • Geometry
  • Summarize (Describe)
  • Compare (Analogy)
  • Critique
  • A Theorem
  • An math tool
  • Future Developments

Change the Verb

  • Instead of asking students to describe how FDR handled the economy during the Depression, ask them to rank four given economic principles in order of importance as they imagine FDR would rank them, then ask them how President Hoover who preceded FDR would have ranked those same principles differently.

 Analyze… Construct…

  •  Analyze… Construct…
  • Revise… Rank…
  • Decide between… Argue against…
  • Why did… Argue for…
  • Defend… Contrast…
  • Devise… Develop…
  • Identify… Plan…
  • Classify… Critique…
  • Define… Rank…
  • Compose… Organize…
  • Interpret… Interview…
  • Expand… Predict…
  • Develop… Categorize…
  • Suppose… Invent…
  • Imagine… Recommend…

Thinking Critically with Gifted Students

  • No matter what readiness level, we teach essential and enduring knowledge first.
  • Gifted experiences illuminate more material during the course of the year, whether by moving more rapidly, by exploring concepts in greater depth, or by offering more breadth in the field of study.
  • Gifted students encounter higher order thinking skills (analysis, synthesis, evaluation, application, justification) as standard operating procedure.
  • In gifted experiences, tangential thinking is invited.
  • Subjects are integrated to a larger extent.
  • Assessment is more authentic and alternative assessment is more likely to occur in gifted experiences.
  • Instruction can be differentiated in terms of changing focus on concept’s depth, frequency, assessment, and/or multi-dimensional understanding.

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